CN107615186A

CN107615186A - The method and apparatus of Model Predictive Control

Info

Publication number: CN107615186A
Application number: CN201580001162.XA
Authority: CN
Inventors: 闫正; 毕舒展
Original assignee: Huawei Technologies Co Ltd
Current assignee: Huawei Technologies Co Ltd
Priority date: 2015-08-13
Filing date: 2015-08-13
Publication date: 2018-01-19
Also published as: WO2017024583A1

Abstract

A kind of method and apparatus of Model Predictive Control, this method include：It is determined that in the parametric variable θ (k) (S110) at k moment；Pass through individual layer recurrent neural network algorithm, according to the control variable u (k 1) at the moment of k 1, the state variable x (k) and parametric variable θ (k) at k moment, it is determined that meeting the controlling increment Δ u (k) (S120) of forecast model performance indications；The control variable u (k 1) of the forecast model and controlling increment Δ u (k) sums are defined as control variable u (k) (S130) of the forecast model at the k moment；According to the control variable u (k) of the forecast model, Model Predictive Control (S140) is carried out.According to the state variable x (k) at moment at current time k and parametric variable θ (k), and the control variable u (k 1) of previous moment, pass through individual layer recurrent neural network algorithm, it is determined that meet the control variable u (k) of forecast model performance indications, according to the control variable u (k), carry out Model Predictive Control, it is possible to increase computational efficiency, it is ensured that the reliability of performance indications.

Description

Method and device for model predictive control

Technical Field

The invention relates to the technical field of information, in particular to a method and a device for model predictive control.

Background

Model Predictive Control (MPC) is a Control strategy that adopts finite time domain multi-step prediction, rolling optimization and feedback correction, and is widely applied to multiple fields of networked Control, resource scheduling management and the like. The MPC has the core idea that the states of N finite moments in the future of a controlled system are predicted at each sampling moment, and then an optimal control signal at the current moment is obtained by solving a finite time domain optimal control problem.

For a general discrete system model x (k +1) ═ f (x (k), u (k)), where x is an n-dimensional state variable, u is an m-dimensional control signal, f denotes the system model, k is the current sampling instant, and k +1 denotes the next sampling instant. The MPC problem for this system can be described as:

s.t.x(k+j+1)＝f(x(k+j),u(k+j)),j＝1,...,N-1

u_min≤u(k+j)≤u_max,j＝0,...,N-1

x_min≤x(k+j)≤x_max,j＝1,...,N

wherein J (k) is a performance index of the control system, Q and R are coefficient matrixes, and can be set as corresponding matrixes according to practical application; f (x (k + N)) is a function on the state variable x (k + N), which can be set according to practical applications; u. of_maxAnd u_minUpper and lower bounds, x, of constraints of the control input, respectively_maxAnd x_minRespectively, an upper bound and a lower bound of the constraint of the system state, and N is a prediction step size.

Specifically, consider a linear variable parameter system x (k +1) ═ a (θ (k)) x (k)) + B (θ (k)) u (k), where θ is an uncertain parameter of dimension p. Generally, the parameter variable θ (k) at the current moment can be measured, and the value range of θ at any moment in the future is known but the specific function expression of the value range is unknown. For the MPC problem with the uncertain parameter system, a widely adopted technical scheme is a min-max optimization method, namely, the worst case caused by the possible influence of all theta is optimized and designed. By optimizing the upper bound of the objective function, the MPC problem of the linear variable parameter system is converted into the optimization problem of the linear matrix inequality by adopting a tool of the linear matrix inequality:

min_γ,Q,Y,X,Lγ

where denotes the corresponding entry of the symmetric matrix and s denotes the number of possible occurrences of theta. After the matrix inequality optimization problem is solved at each sampling time, the optimal control signal of the control system is u (k) ═ YQ^-1x(k)。

The biggest problem with this technique is its computational conservatism. The optimal control signals are designed under the framework of MPC with the goal of achieving the best performance for the system-specific performance metrics. The existing minimum-maximum (min-max) optimization scheme considers the worst possible situation of the system, but for the controlled object, the expression form of each moment is determined and the worst situation is not always presented. In this case, the worst case of the performance index is optimized, and the overall control performance is undoubtedly sacrificed. In addition, the obtaining of the optimal control signal of the MPC is based on the optimization of the future predicted state of the system, and if a large error exists between the model f (x, u) of the controlled system and the actual controlled object, the obtained optimal control signal has difficulty in obtaining a satisfactory control effect.

Disclosure of Invention

The invention provides a method and a device for model predictive control, which can improve the calculation efficiency and ensure the reliability of performance indexes of the model predictive control.

In a first aspect, a method for model predictive control is provided, the method comprising: determining a parameter variable theta (k) at the k moment according to at least one of parameter variables theta (k-1) to theta (k-q) of the prediction model at the k-1 moment to the k-q moment, a state variable x (k) at the k moment and a control variable u (k-1) at the k-1 moment; solving a quadratic programming problem on line by a single-layer recurrent neural network algorithm, and determining a control increment delta u (k) meeting the performance index of the prediction model according to the state variable x (k), the control variable u (k-1) and the parameter variable theta (k); determining a control variable u (k) of the predictive model at the time k according to the control variable u (k-1) and the control increment Δ u (k) of the predictive model, wherein u (k) is u (k-1) + Δ u (k); and performing model predictive control according to the control variable u (k) of the predictive model.

With reference to the first aspect, in an implementation manner of the first aspect, the determining the parameter variable θ (k) at the time k according to at least one of the parameter variables θ (k-1) to θ (k-q) of the prediction model from the time k-1 to the time k-q, the state variable x (k) at the time k, and the control variable u (k-1) at the time k-1 includes determining a model function θ (α) of the single hidden layer neural network, determining an input parameter α (k) ═ x (k); u '(k); θ (k-1); θ (k-q) ], where q is an integer and 1. ltoreq. q < k, and calculating the parameter variable θ (k) by substituting the input parameter α (k) into the model function α, based on the state variable x (k) of the prediction model, the predicted control variable u' (k) at the time k) and the parameter variables θ (k-1) to the time k-q.

With reference to the first aspect and the foregoing implementation manner of the first aspect, in another implementation manner of the first aspect, the determining the model function θ (α) of the single hidden layer neural network includes determining s sets of input data α ═ α₁，…,α_s]And corresponding s sets of output data θ ═ θ₁，…,θ_s](ii) a Constructing the single hidden layer neural network, wherein the number of input layer neurons of the single hidden layer neural network is n + m + pq, the number of hidden layer neurons is L, the number of output layer neurons is p, a hidden layer neuron excitation function is g (·), and a weight vector from the ith input layer to the hidden layer is w_iThe bias vector of the neuron is b_iWhere n is the dimension of the state variable x (k) and m is the dimension of the control variable u (k), the input data α being [ α ] according to the single hidden layer neural network₁，…,α_s]And the output data theta ═ theta₁，…,θ_s]Determining the weight parameter β of the neuron of the single hidden layer neural network connected with the output layerH^T(I+HH^T)^-1[θ₁,...,θ_s]Wherein:

determining the model function θ (α):

wherein, β_iLine i of the weight parameter β.

With reference to the first aspect and the foregoing implementation manner of the first aspect, in another implementation manner of the first aspect, the method further includes: determining the state variable x (k + N) of the prediction model at the time k + N according to the parameter variable theta (k) at the time k, the state variable x (k) and the predicted control variable u' (k + N-1) at the time k + N-1 by the following formula:

x(k+N)＝A(θ(k+N-1))x(k+N-1))+B(θ(k+N-1))u'(k+N-1))

where A (theta (-)) is a first reference function for theta (-) and B (theta (-)) is a second reference function for theta (-) with N being a time step and N being a positive integer, determining an input parameter α (k + N) [ [ x (k + N) ] (k + N) ], theta (k + N-1) ], where q is an integer and 1 ≦ q < k ], from the state variable x (k + N), the predicted control variable u' (k + N) at the time k + N, and the parameter variables theta (k + N-1) through theta (k + N-q) at the time k + N-q, and substituting the input parameter α (k + N) into the model function theta (α) to calculate the parameter theta (k + N) at the time k + N.

With reference to the first aspect and the foregoing implementation manner, in another implementation manner of the first aspect, the solving a quadratic programming problem on line by using a single-layer recurrent neural network algorithm, and determining a control increment Δ u (k) that satisfies a performance index of the prediction model according to the state variable x (k), the control variable u (k-1), and the parameter variable θ (k), includes: determining, by the single-layer recurrent neural network algorithm, the control increment Δ u (k) according to the following equation:

wherein the content of the first and second substances,

a (theta (-) is a first reference function for theta (-) and B (theta (-)) is a second reference function for theta (-) and a matrix of the last n rows S, V and M, respectively, n being the dimension of the state variable x (k), -u_min+ u (k-1) is-u for each row_minM-row matrix of + u (k-1), u_max-u (k-1) is u for each row_maxAn m-row matrix of u (k-1), m being the dimension of the control variable u (k), λ being a positive real number, u_maxAnd u_minMaximum and minimum values of control variables, x, representing the predictive model_maxAnd x_minRepresenting the maximum value and the minimum value of the state variable of the prediction model, Q and R are any positive definite diagonal matrix, and P satisfies the following inequality:

Q+K^TRK+(A(θ(k+1))+B(θ(k+1))K)^TP(A(θ(k+1))+B(θ(k+1))K)-P≤0

wherein P >0 and K is an auxiliary variable.

With reference to the first aspect and the foregoing implementation manner of the first aspect, in another implementation manner of the first aspect, the method further includes: solving a quadratic programming problem on line by the single-layer recurrent neural network algorithm, and determining the control increment from the k moment to the k + N-1 moment according to the following formula

Wherein the content of the first and second substances,

Δ u (k + j) ═ u (k + j) -u (k + j-1) ], 0 ≦ j ≦ N, a (θ (·)) is a first reference function with respect to θ (·), B (θ (·)) is a second reference function with respect to θ (·), and matrices formed by the last N rows of S, V and M, respectively, N is a dimension of the state variable x (k), is a matrix of M × N rows for each row, M is a dimension of the control variable u (k), N is a time step, λ is a positive real number, and control variable maximum and minimum values representing the prediction model, and state variable maximum and minimum values representing the prediction model, Q and R are arbitrary positive diagonal matrices, P satisfies the following inequality:

Q+K^TRK+(A(θ(k+N))+B(θ(k+N))K)^TP(A(θ(k+N))+B(θ(k+N))K)-P≤0

wherein P >0 and K is an auxiliary variable.

With reference to the first aspect and the foregoing implementation manner of the first aspect, in another implementation manner of the first aspect, the method further includes: and determining the control variable from the k moment to the k + N-1 moment according to the control increment from the k moment to the k + N-1 moment and the control variable from the k-1 moment to the k + N-2 moment, wherein model prediction control is carried out according to the control variable from the k moment to the k + N-1 moment.

In a second aspect, there is provided an apparatus for model predictive control, the apparatus comprising: a first determining module, which is used for determining a parameter variable theta (k) at the k moment according to at least one of the parameter variables theta (k-1) to theta (k-q) of the prediction model at the k-1 moment to the k-q moment, a state variable x (k) at the k moment and a control variable u (k-1) at the k-1 moment; the second determining module is used for solving a quadratic programming problem on line through a single-layer recurrent neural network algorithm, and determining a control increment delta u (k) meeting the performance index of the prediction model according to the state variable x (k), the control variable u (k-1) and the parameter variable theta (k) determined by the first determining module; a third determining module, configured to determine a control variable u (k) of the predictive model at the time k according to the control variable u (k-1) of the predictive model and the control increment Δ u (k) determined by the second determining module, where u (k) is u (k-1) + Δ u (k); and the control module is used for carrying out model prediction control according to the control variable u (k) of the prediction model determined by the third determination module.

With reference to the second aspect and the foregoing implementation manner of the second aspect, in another implementation manner of the second aspect, the first determining module is specifically configured to determine that the s sets of input data α are [ α ]₁，…,α_s]And corresponding s sets of output data θ ═ θ₁，…,θ_s](ii) a Constructing the single hidden layer neural network, wherein the number of input layer neurons of the single hidden layer neural network is n + m + pq, the number of hidden layer neurons is L, the number of output layer neurons is p, a hidden layer neuron excitation function is g (·), and a weight vector from the ith input layer to the hidden layer is w_iThe bias vector of the neuron is b_iWhere n is the dimension of the state variable x (k) and m is the dimension of the control variable u (k), the input data α being [ α ] according to the single hidden layer neural network₁，…,α_s]And the output data theta ═ theta₁，…,θ_s]Determining the weight parameter β ═ H of the connection between the neuron of the single hidden layer neural network and the output layer^T(I+HH^T)^-1[θ₁,...,θ_s]Wherein:

determining the model function θ (α):

wherein, β_iLine i of the weight parameter β.

With reference to the second aspect, in an implementation manner of the second aspect, the first determining module is specifically configured to determine a model function θ (α) of the single hidden layer neural network, determine an input parameter α (k) ═ x (k), u '(k), θ (k-1) · θ (k-q) ], where q is an integer and 1 ≦ q < k, according to the state variable x (k) of the prediction model, the prediction control variable u' (k) at the time k, and the parameter variables θ (k-1) to θ (k-q) from the time k-1 to the time k-q, and substitute the input parameter α (k) into the model function θ (α) to calculate the parameter variable θ (k) at the time k.

With reference to the second aspect and the foregoing implementation manner of the second aspect, in another implementation manner of the second aspect, the first determining module is specifically configured to: determining the state variable x (k + N) of the prediction model at the time k + N according to the parameter variable theta (k) at the time k, the state variable x (k) and the predicted control variable u' (k + N-1) at the time k + N-1 by the following formula:

x(k+N)＝A(θ(k+N-1))x(k+N-1))+B(θ(k+N-1))u'(k+N-1))

With reference to the second aspect and the foregoing implementation manner of the second aspect, in another implementation manner of the second aspect, the second determining module is specifically configured to: determining, by the single-layer recurrent neural network algorithm, the control increment Δ u (k) according to the following equation:

wherein the content of the first and second substances,

a (theta (-) is a first reference function with respect to theta (-) and B (theta (-)) is a second reference function with respect to theta (-) and S, V and M, respectivelyA matrix of the last n rows, n being the dimension of the state variable x (k), -u_min+ u (k-1) is-u for each row_minM-row matrix of + u (k-1), u_max-u (k-1) is u for each row_maxAn m-row matrix of u (k-1), m being the dimension of the control variable u (k), λ being a positive real number, u_maxAnd u_minMaximum and minimum values of control variables, x, representing the predictive model_maxAnd x_minRepresenting the maximum value and the minimum value of the state variable of the prediction model, Q and R are any positive definite diagonal matrix, and P satisfies the following inequality:

Q+K^TRK+(A(θ(k+1))+B(θ(k+1))K)^TP(A(θ(k+1))+B(θ(k+1))K)-P≤0

wherein P >0 and K is an auxiliary variable.

With reference to the second aspect and the foregoing implementation manner of the second aspect, in another implementation manner of the second aspect, the second determining module is further configured to: determining the control increment from the k time to the k + N-1 time according to the following formula by the single-layer recurrent neural network algorithm

Wherein the content of the first and second substances,

Q+K^TRK+(A(θ(k+N))+B(θ(k+N))K)^TP(A(θ(k+N))+B(θ(k+N))K)-P≤0

wherein P >0 and K is an auxiliary variable.

With reference to the second aspect and the foregoing implementation manner of the second aspect, in another implementation manner of the second aspect, the third determining module is further configured to: and determining the control variable from the k moment to the k + N-1 moment according to the control increment from the k moment to the k + N-1 moment and the control variable from the k-1 moment to the k + N-2 moment, wherein model prediction control is carried out according to the control variable from the k moment to the k + N-1 moment.

Based on the technical scheme, the method and the device for model predictive control in the embodiment of the invention determine the control increment delta u (k) meeting the performance index of the predictive model through a single-layer recurrent neural network algorithm according to the state variable x (k) and the parameter variable theta (k) at the current moment k and the control variable u (k-1) at the previous moment k-1, wherein the sum of the control increment delta u (k) and the control variable u (k-1) at the moment k-1 is the control variable u (k) at the current moment k, and finally, the model predictive control is performed according to the control variable u (k). Therefore, the control variable at the current moment which is more optimized than that in the prior art can be obtained, so that the calculation efficiency can be improved, the accuracy of the performance index is theoretically ensured, the closed-loop control system is gradually stable, the whole model prediction control system runs highly autonomously, and the automatic operation is realized.

Drawings

In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the embodiments of the present invention will be briefly described below, and it is obvious that the drawings described below are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without creative efforts.

FIG. 1 is a schematic flow chart diagram of a method of model predictive control in accordance with an embodiment of the invention.

FIG. 2 is a schematic diagram of a single hidden layer neural network structure according to an embodiment of the present invention.

FIG. 3 is a schematic illustration of a comparison of control variables for a mass spring system according to an embodiment of the invention.

FIG. 4 is a schematic illustration of a state variable comparison of a mass spring system according to an embodiment of the invention.

FIG. 5 is a schematic block diagram of an apparatus for model predictive control in accordance with an embodiment of the invention.

FIG. 6 is another schematic block diagram of an apparatus for model predictive control in accordance with an embodiment of the invention.

Detailed Description

The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, not all, embodiments of the present invention. All other embodiments, which can be obtained by a person skilled in the art without any inventive step based on the embodiments of the present invention, shall fall within the scope of protection of the present invention.

FIG. 1 shows a schematic flow diagram of a method 100 of model predictive control in accordance with an embodiment of the invention. As shown in fig. 1, the method 100 includes:

s110, determining a parameter variable theta (k) at the k moment according to at least one of parameter variables theta (k-1) to theta (k-q) of a prediction model from the k-1 moment to the k-q moment, a state variable x (k) at the k moment and a control variable u (k-1) at the k-1 moment;

s120, solving a quadratic programming problem on line through a single-layer recurrent neural network algorithm, and determining a control increment delta u (k) meeting the performance index of the prediction model according to the state variable x (k), the control variable u (k-1) and the parameter variable theta (k);

s130, determining the control variable u (k) of the prediction model at the time k according to the control variable u (k-1) and the control increment Δ u (k) of the prediction model, wherein u (k) is u (k-1) + Δ u (k);

s140, according to the control variable u (k) of the prediction model, model prediction control is carried out.

Specifically, a state variable x (k) of a prediction model at a moment k and a control variable u (k-1) of the prediction model at a moment k-1 are obtained, and a parameter variable theta (k) at the moment k is determined according to the state variable x (k) and the control variable u (k-1), and optionally, the parameter variable theta (k) can be determined by training a model of a single hidden layer neural network; determining a control increment delta u (k) meeting the performance index of the prediction model according to a state variable x (k), a control variable u (k-1) and a parameter variable theta (k) by using a single-layer recurrent neural network algorithm, wherein the sum of the control increment delta u (k) and the control variable u (k-1) at the moment k-1 is the control variable u (k) at the moment k, and performing model prediction control through the control variable at the moment k.

Alternatively, the method of the embodiment of the present invention may be implemented by a neural network architecture, for example, the prediction process for determining the parameter variable θ (k) and the online optimization process for determining the control increment Δ u (k) in the method may be implemented by the neural network architecture, and the neural network architecture may be implemented by a neuromorphic computing chip, which is not limited in the present invention.

Therefore, in the method for model predictive control according to the embodiment of the present invention, a control increment Δ u (k) meeting the performance index of the predictive model is determined by a single-layer recurrent neural network algorithm according to the state variable x (k) and the parameter variable θ (k) at the current time k and the control variable u (k-1) at the previous time k-1, and the sum of the control increment Δ u (k) and the control variable u (k-1) at the time k-1 is the control variable u (k) at the current time k, and finally, model predictive control is performed according to the control variable u (k). Therefore, the control variable at the current moment which is more optimized than that in the prior art can be obtained, so that the calculation efficiency can be improved, the accuracy of the performance index is theoretically ensured, the closed-loop control system is gradually stable, the whole model prediction control system runs highly autonomously, and the automatic operation is realized.

In the embodiment of the present invention, for a control problem with optimization requirement, the model embodied in the controlled object may be represented in the form of formula (1):

x(k+1)＝A(θ(k))x(k)+B(θ(k))u(k) (1)

wherein x (k) is a state variable of the system at the current moment k, and can be obtained by real-time measurement in the controlled process; u (k) is the control variable of the system at the current moment k, i.e. the control signal, which is currently unknown; a (theta (-) and B (theta (-))) are reference functions related to a parameter variable theta (k) in a controlled process, and can be regarded as a parameter matrix form, the specific form of the parameter matrix depends on the value of the parameter variable theta (k), and theta (k) can be measured in real time from the controlled process. The control problem has a known target output, and the control target is to make the actual output of the controlled process and the target output nearly equal by designing u (k).

Optionally, a typical use case of the embodiment of the present invention includes: resource management of a data center, automatic control of a robot, supply chain management of semiconductor production, building energy-saving control, unmanned aerial vehicle flight control and the like. One of the common features of these use cases is that their control objectives are to achieve an optimization of some performance metric describing the global system behavior, while the constraints of the physical conditions define the range of control actions that can be taken. To the extent feasible, there is always a control action such that the performance index describing the global system takes a minimum. For example, for resource management of a data center, an important global performance index is the overall system energy consumption, in this case, the state variables of the predictive control may include the temperature, the power consumption, or the resource utilization rate of the data center, and the control signals may be the rotation speed of the fan/air conditioner, CPU thread allocation instructions, and the like, but the present invention is not limited thereto.

In S110, a parameter variable theta (k) at the k time is determined according to at least one of parameter variables theta (k-1) to theta (k-q) of the prediction model at the k-1 time to the k-q time, a state variable x (k) at the k time, and a control variable u (k-1) at the k-1 time. Specifically, the model of the controlled object can be expressed as shown in formula (1), wherein a state variable of the controlled object at the current time k and a control variable of the controlled object at the previous time k-1 can be obtained in real time through measurement; the parameter variable θ (k) may be determined according to at least one of the parameter variables θ (k-1) to θ (k-q) of the prediction model from the time k-1 to the time k-q, the state variable x (k) at the time k, and the control variable u (k-1) at the time k-1, specifically, the parameter variable θ (k) may be determined by using the prior art, or may be determined by using a single hidden layer neural network in the embodiment of the present invention, which is not limited thereto.

The neural network adjusts the interconnection relationship among a large number of neurons therein by means of a learning algorithm thereof, thereby achieving a specific calculation purpose, firstly, a model function theta (α) of the single hidden layer neural network can be determined, and particularly, an input parameter α (k) can be defined by the following formula (2):

θ(k)＝F(x(k),u(k),θ(k-1),...,θ(k-q))＝F(α(k)) (2)

that is, for the parameter variable θ (k) at the current time, it can be expressed as a function F (α (k)) with respect to the input parameter α (k), and since the input of the function is α (k), the output is the parameter variable θ (k), i.e., it can be expressed as a model function θ (α), where the input parameter α (k) satisfies the following equation (3):

α(k)＝[x(k)；u'(k)；θ(k-1)；...；θ(k-q)] (3)

wherein, x (k) is a state variable at the current moment k; u' (k) is a predicted amount of the controlled variable at the present time, i.e., a predicted controlled variable; the parameter variables from time k-1 to time k-q are theta (k-1) to theta (k-q), where q is a time constant, which can be defined by the user.

First, the controlled object is analyzed off-line, and two groups of data theta (theta) (α) can be obtained₁，…,θ_s]And α ═ α₁，…,α_s]Where s is the number of sample data, defined by the user, the greater the number of samples, the greater the accuracy, but the higher the sampling cost, so a reasonable number of samples can be determined empirically, hi addition, each α and θ here have a one-to-one correspondence, i.e., for each input α_iCorrespondingly, an output θ can be obtained_i。

As shown in fig. 2, a single hidden layer neural network is constructed. The number of neurons of an input layer of the single hidden layer neural network is n + m + pq, n is the dimension of a state variable x (k), and m is the dimension of a control variable u (k); the number of neurons in an output layer is p, and p is the dimension of theta (k); the number of hidden layer neurons is L, the value of L can beDefined by a user; the hidden layer neuron excitation function is g (·), which can be determined by empirical values; the weight vector from the ith input layer to the hidden layer is w_iThe bias vector of the neuron is b_i，w_iAnd b_iCan be randomly generated.

Input parameter α ═ α in the sample₁，…,α_s]Substituting into the following equation (4), a neuron matrix H is obtained:

obtaining matrix H and output theta in s samples ═ theta₁，…,θ_s]Substituting the weight parameter β of the neuron of the single hidden layer neural network connected with the output layer into the following formula (5):

β＝H^T(I+HH^T)^-1[θ₁,...,θ_s] (5)

it may be determined that the model function θ (α) of the single hidden layer neural network that has completed training is represented by equation (6):

wherein, β_iRow i of the matrix of weight parameters β.

Therefore, at the current time k, the parameter variable θ (k) at the time k can be obtained by inputting the input parameter α (k) defined by the equation (3) and substituting the input parameter into the equation (6).

In the embodiment of the present invention, after the parameter variable θ (k) at time k is determined, the parameter variable θ (k) may be substituted into formula (1), the state variable x (k +1) at time k +1 may be determined, and then the parameter variable θ (k +1) at time k +1 may be determined according to the predicted control variable u' (k +1) at time k +1, and so on, where N is the prediction step for determining the parameter variable θ (k + N) at time k + N at any time. First, from the parameter variable θ (k) at time k and the predicted control variable u' (k + N-1) at time k + N-1, the state variable x (k + N) at time k + N can be obtained by the following equation (7):

x(k+N)＝A(θ(k+N-1))x(k+N-1)+B(θ(k+N-1))u'(k+N-1) (7)

the formula (7) is a modified form of the formula (1) at the time k + N, a (θ (-)) is a first reference function with respect to θ (-) and B (θ (-) is a second reference function with respect to θ (-) with N being a positive integer.

For the determined state variable x (k + N) at time k + N and the predicted controlled variable u (k + N) at time k + N, the input parameter α (k + N) may be similarly determined by equation (3) as shown in equation (8):

α(k+N)＝[x(k+N)；u'(k+N)；θ(k+N-1)；...；θ(k+N-q)] (8)

by substituting the input parameter α (k + N) into equation (6), the parameter variable θ (k + N) at the time of k + N can be obtained.

In the embodiment of the invention, the unknown parameters are modeled and estimated by using the single hidden layer neural network, so that the problem of model mismatch in the predictive control of the linear variable parameter system is better solved. The neural network is simple in structure and high in training speed, avoids complex iterative training of the traditional neural network, and improves the calculation efficiency.

In S120, a quadratic programming problem is solved on line by a single-layer recurrent neural network algorithm, and a control increment Δ u (k) satisfying the performance index of the prediction model is determined according to the state variable x (k), the control variable u (k-1) and the parameter variable θ (k). Specifically, for the controlled system as expressed in equation (1), several parameters from time k to time k + N may be defined, as expressed in equation (9) below:

the matrix is a matrix formed by state variables x (k +1) to x (k + N) from the moment k +1 to the moment k + N; the matrix is formed by control variables u (k) to u (k + N-1) from time k to time k + N-1; the matrix is a matrix formed by control increments Δ u (k) to Δ u (k + N-1) from time k to time k + N-1, and for any control increment Δ u (k + j), it can be expressed as shown in equation (10):

Δu(k+j)＝u(k+j)-u(k+j-1) (10)

then, according to equation (9) and equation (10), equation (1) can be expressed as shown by the following equation (11):

wherein the matrices S, V and M are respectively expressed as shown in the following equation (12):

wherein, A (theta (-)) is a first reference function related to theta (-) and B (theta (-)) is a second reference function related to theta (-) and is related to a controlled object; θ (-) may be a parameter variable at each time determined in S110.

In the embodiment of the present invention, the performance index of MPC is expressed as shown in the following equation (13):

wherein Q and R are arbitrary positive definite diagonal matrices, which can be selected by user definition, and P satisfies the following inequality (14):

Q+K^TRK+(A(θ(k+N))+B(θ(k+N))K)^TP(A(θ(k+N))+B(θ(k+N))K)-P≤0

P>0 (14)

wherein K is an auxiliary variable.

Substituting equation (11) into equation (13) may obtain a constrained optimization problem of the performance index of the controlled object, which may be expressed as the following equation (15):

wherein each parameter further satisfies the following formula (16):

where n is the dimension of the state variables x (k), and the unit matrix of the maximum and minimum values of the control variables representing the predictive model, and the maximum and minimum values of the state variables representing the predictive model, and the maximum and minimum values of the control increments representing the predictive model, and n x n.

Several matrix forms are defined as in equation (17) below:

wherein, the matrix is an m × N row matrix for each row, and the matrix is an m × N row matrix for each row.

The performance index as shown in equation (15) can be expressed as shown in equation (18) below according to equation (17):

the corresponding equation (17) can be expressed as shown in equation (19):

by designing a single-layer recurrent neural network, a quadratic programming problem can be solved on line, namely a constraint optimization problem can be solved on line, a model and a self-learning method of the neural network can be defined by the following formula (20), namely, a control increment from the time k to the time k + N-1 in the formula (9) is determined according to the following formula (20)

Where λ is a sufficiently large positive real number, and its specific value can be defined by the user. Through an optimization theory and a neurodynamics related theory, the neural network can be converged to a global optimal solution of a corresponding constraint optimization problem from any initial state.

In the embodiment of the present invention, the control increment from the time k to the time k + N-1 may be determined by the above equation (20), for example, the control increment Δ u (k) at the time k may be obtained by substituting N in 1 into the above equation (20), and the control increment Δ u (k) at the time k at the current time may be determined by using the above equation (20).

In the embodiment of the invention, the optimal control variable, namely the optimal control signal, is calculated on line by using the recurrent neural network, so that the calculation efficiency is high and the real-time performance is good. In addition, the number of the neurons of the neural network and a learning algorithm are quantitatively and qualitatively provided, the implementation is simple and convenient, and the internal parameters do not need to be manually adjusted.

In S130, the control variable u (k) of the prediction model at the time k is determined according to the control variable u (k-1) and the control increment Δ u (k) of the prediction model, where u (k) is u (k-1) + Δ u (k). Specifically, for the control increment from time k to time k + N-1 determined in S130, for example, for the control increment Δ u (k) at time k, since equation (9) is satisfied, the determined control increment Δ u (k) is summed with the obtained control variable u (k-1) at time k-1, the control variable u (k) at the current time may be obtained, and by analogy, the control increment for time k + N-1 may be summed with the obtained control variable u (k + N-2) at time k + N-2, and the control variable u (k + N-1) at time k + N-1 may be obtained, and the present invention is not limited thereto.

In the embodiment of the present invention, the control variable u (k + N-1) at the time k + N-1 and the state variable x (k + N-1) obtained by real-time measurement are substituted into the formula (7), so that the state variable x (k + N) at the time k + N can be obtained, and by analogy, the state variable and the control variable at the time k and any time after the time k are obtained, which is not limited in this respect.

In S140, model predictive control is performed based on the control variables u (k) of the predictive model.

It should be understood that, in various embodiments of the present invention, the sequence numbers of the above-mentioned processes do not mean the execution sequence, and the execution sequence of each process should be determined by its function and inherent logic, and should not constitute any limitation on the implementation process of the embodiments of the present invention.

The MPC process of the mass-spring system will be exemplified as follows. Specifically, as known from the law of motion of the controlled system, the prediction model can be written as the following formula (21):

x(k+1)＝A(θ(k))x(k))+Bu(k)) (21)

that is, for the general expression form of the controlled object model as formula (1), a form as shown in formula (21) can be written in the mass-spring system, wherein the specific forms of the first reference function a (θ (k)) and the second reference function B are as shown in the following formula (22):

in this mass-spring system, it is assumed that the initial state of the measurement system yields x (0) ═ 1; 1; 0; 0 ]; the control target is to stabilize the system state variable to zero; the state variable may be a velocity or an acceleration, etc., and the control variable may be an applied external force, but the present invention is not limited thereto. Specifically, the implementation process of the control method of the embodiment of the invention on the mass spring system is as follows:

first, according to equation (9), several unknown parameters from the current time k to the future time k +20 are defined, as shown in equation (23):

the matrix is a matrix formed by state variables x (k +1) to x (k +20) from the moment k +1 to the moment k + 20; the matrix is formed by control variables u (k) to u (k +19) from time k to time k + 19; the matrix is a matrix formed by control increments Δ u (k) to Δ u (k +19) from time k to time k +19, and can be expressed as shown in equation (10) for any control increment Δ u (k + j).

Second, by transforming equation (21) according to equation (11), the parameter matrices S, V and M defined according to equation (12) can be written as shown in equation (24) below:

wherein A (θ (k + i)) satisfies the following formula (25):

third, a single hidden layer neural network is constructed, and a parameter variable θ (k) is determined, specifically, an input parameter α (k) is defined according to formula (3), where q is 1, a state variable x (k) at the current time k is obtained, and a control variable at the predicted time k is u' (k), then it may be determined that the input parameter α (k) is expressed as shown in formula (26):

α(k)＝[x(k)；u'(k)；θ(k-1)] (26)

first, in the controlled system, i.e., the mass-spring system, 2000 sets of sample data including 2000 sets of input data α ═ α were measured₁，…,α₂₀₀₀]And the output data theta [ theta ] corresponding to the 2000 groups₁，…,θ₂₀₀₀]The specific numerical value of (1).

Secondly, designing a single hidden layer neural network, and enabling the number of neurons of an input layer to be 6 according to the state of a controlled system and the dimensionality of input data; setting the number of the hidden layers to be 1000, which can be defined by a user; the number of neurons in the output layer is 1.

Thirdly, randomly generating a weight vector w from the input layer to the hidden layer_iThe bias vector of the neuron is b_i. The neuron matrix H can be obtained by substituting the excitation function g (·) for each neuron into equation (4) and the above parameters. The matrix H and the output data theta of 2000 groups of sample data are equal to [ theta%₁，…,θ₂₀₀₀]Substituted into equation (5), determinedThe model function theta (α) for the α single hidden layer neural network can be obtained by outputting layer weight parameters β and substituting β into equation (6).

Finally, the input parameters α (k) determined by the formula (26) are substituted into the determined model function θ (α) of the single hidden layer neural network, and the parameter variable θ (k) can be obtained.

Fourth, by substituting the state variable x (k) at the time k at the present time, the obtained parameter variable θ (k), and the predicted control variable u' (k) into equations (21) and (22), the state variable x (k +1) at the time k +1 can be obtained, the input parameter in equation (26) is updated, and the input parameter α (k +1) at the time k +1 is obtained as shown in the following equation (27):

α(k+1)＝[x(k+1)；u'(k+1)；θ(k)] (27)

and (3) substituting the input parameters α (k +1) into the determined model function theta (α) of the single hidden layer neural network to correspondingly obtain parameter variables theta (k +1), and circulating the steps to sequentially obtain the parameter variables theta (k +2) and … theta (k + 19).

The parameter variable theta (k) obtained above; … θ (k +19) are sequentially substituted into equation (24), the values of parameter matrices S, V and M can be obtained, respectively.

Fifth, taking the Q and R matrices as identity matrices, and substituting the above-mentioned parameters into inequality (14), a matrix P can be obtained, and specifically, the specific expression of the P matrix is shown in the following formula (28):

sixthly, the values of the parameter matrices S, V and M determined as described above are substituted into equation (17) according to the optimization problem described in equation (15) to obtain specific values of W, p, E, and b.

Seventhly, the specific values of the determined W, p, E and b are substituted into the formula (20), and the control increment from the time k to the time k +19 is calculated and obtained

Eighth, a matrix formed by the control variables u (k) to u (k +19) from the time k to the time k +19 is calculated according to the formula (10), and finally, the determined control variables are applied to the controlled system.

Optionally, in the seventh step, the control increment Δ u (k) at the time k at the current time may be determined according to the formula (20), and further, the optimal control variable u (k) at the time k may be determined; the value of k is updated by setting k to k +1, and the third to seventh steps in the above steps are repeated until the value of k reaches the end of the control time, for example, k to k + 10.

In the embodiment of the present invention, the mass spring system is controlled by the above method, and the calculated control variable u (-) is shown by a solid line in fig. 3, and the broken line is the control variable u (-) determined by a linear quadratic regulator (abbreviated as "LQR") of the related art. In addition, if the controlled system is controlled according to the control variable, as shown in fig. 4, the solid line is a change curve x (k) of the state variable and time obtained by the embodiment of the present invention, and the dotted line is a curve x (k) of the state variable and time determined by LQR.

As can be seen from fig. 4, the state variable obtained by the embodiment of the present invention tends to zero faster than LQR, that is, the method of the embodiment of the present invention makes the spring system calm to the zero state faster, and the effect is obviously better than LQR.

Therefore, in the method for model predictive control according to the embodiment of the present invention, a control increment Δ u (k) meeting the performance index of the predictive model is determined by a single-layer recurrent neural network algorithm according to the state variable x (k) and the parameter variable θ (k) at the current time k and the control variable u (k-1) at the previous time k-1, and the sum of the control increment Δ u (k) and the control variable u (k-1) at the time k-1 is the control variable u (k) at the current time k, and finally, model predictive control is performed according to the control variable u (k). Therefore, the control variable at the current moment which is more optimized compared with the prior art can be obtained, the calculation efficiency can be improved, the accuracy of the performance index is theoretically ensured, the closed-loop control system is gradually stable, the whole model prediction control system runs highly autonomously, and the automatic operation is realized.

The following will illustrate how the model predictive control method of the present invention can be used to optimize the temperature and humidity of a data center by taking the ventilation and air conditioning system of a data center as an example. Specifically, let W_zIndicating the room temperature, T_zIndicating the room temperature, T_secRepresenting the secondary coil temperature, representing the rate of air inflow, the state vector of the control system can be expressed as a model of the control that can be modeled from a priori knowledge as shown in equation (1), where a (θ (k)) and B (θ (k)) are shown in equation (29) below:

wherein, V_zIs a zone volume (W)_priIs the primary air humidity (moisture content of the primary air), W_z,opIs zone humidity (zone humidity content), τ_vIs the time constant of the valve (time constant of the valve) and ε is the gain constant (gain constant).

In addition, let u ═ ρ; t is_z,in]Where ρ is the opening amplitude of the switching valve, T_z,inIs the temperature of the inlet chilled water. Assuming the current temperature of the data center is 25 degrees, the humidity is 10.25 x 10^-3The control targets are that the indoor temperature is changed to 24 degrees and the humidity is changed to 9.25 x 10^-3Then, the specific implementation process of the control method according to the embodiment of the present invention is as follows:

first, according to equation (9), let N be 10, several unknown vectors from the current time k to the future time k +10 are defined, as shown in equation (30):

the matrix is a matrix formed by state variables x (k +1) to x (k +20) from the moment k +1 to the moment k + 10; the matrix is formed by control variables u (k) to u (k +19) from time k to time k + 9; the matrix is a matrix formed by control increments Δ u (k) to Δ u (k +19) from time k to time k +9, and can be expressed as shown in equation (10) for any control increment Δ u (k + j).

Second, substituting equation (10) and equation (30) into equation (1) may result in equation (11), where parameter matrices S, V and M may be written as shown in equation (12).

Thirdly, a single hidden layer neural network is constructed, and parameters are determinedA variable θ (k), where θ (k) is [ θ [ ]₁(k)；θ₂(k)；θ₃(k)；θ₄(k)；θ₅(k)]Specifically, the input parameter α (k) is defined according to equation (3), where q is 1, the state variable x (k) at the current time k is obtained, and the control variable at the time k is predicted to be u' (k), and then it may be determined that the input parameter α (k) is expressed as shown in equation (31):

α(k)＝[x(k)；u'(k)；θ(k-1)] (31)

first, to accurately estimate θ (k), an off-line data collection is performed for the ventilation and air conditioning system of the data center, which may be sampled at 2000 moments to obtain 2000 sets of sample data, i.e., 2000 sets of input data α ═ α₁，…,α₂₀₀₀]And the output data theta [ theta ] corresponding to the 2000 groups₁，…,θ₂₀₀₀]The specific numerical value of (1).

Secondly, designing a single hidden layer neural network, and enabling the number of neurons of an input layer to be 4+2+5 to be 11 according to the state of a controlled system and the dimension of input data; setting the number of hidden layer neurons to be 1000, which can be defined by a user; the number of neurons in the output layer was 5.

Thirdly, randomly generating a weight vector w from the input layer to the hidden layer_iThe bias vector of the neuron is b_i. The neuron matrix H can be obtained by substituting the excitation function g(s) for each neuron into the equation (4) and assigning the parameters to the excitation function g(s) tanh(s). The matrix H and the output data theta of 2000 groups of sample data are equal to [ theta%₁，…,θ₂₀₀₀]The output layer weight parameter β is determined by substituting equation (5), and the model function theta (α) of the single hidden layer neural network with respect to α can be obtained by substituting equation (6) with this β.

Finally, the input parameters α (k) determined according to the formula (31) are substituted into the determined model function θ (α) of the single hidden layer neural network, so that the parameter variable θ (α (k)) can be obtained, and the parameter variable θ (α (k)) can be correspondingly obtained according to α (k).

Fourthly, when the current time k is set to 0, the state variable x (k) ═ x (0) ([ 0.001; 0.012; 1; 5) of the system is measured, and the initial control variable u (k) ═ u (0) ([ 0; 0] is measured, the output signal θ (k), θ (k +1), …, and θ (k +9) can be calculated by substituting α (k), α (k +1), …, α (k +9) as input signals into the model function θ (α (k)) of the single hidden layer neural network of α (k) according to the formula (31).

The parameter variable theta (k) obtained above; θ (k + 1); …, respectively; by substituting θ (k +9) into equation (12), specific values of the parameter matrices S, V and M can be obtained, respectively.

Fifth, let the Q and R matrices be as shown in equation (32) below:

the matrix P can be obtained by substituting the determined parameters of Q, R, K, A (θ (k)) and B (θ (k)) into the inequality (14), and specifically, the specific expression of the P matrix is finally calculated as shown in the following formula (33):

sixthly, according to the optimization problem described by the formulas (15) and (16), the values of the parameter matrixes S, V and M determined above are substituted into the formula (17), wherein the value range of the sum is not limited; and satisfies the following formula (34):

the corresponding equation (17) can be simplified as shown in equation (35):

specific values of W, p, E and b are obtained according to the formula (35).

Seventhly, the specific values of W, p, E, and b thus determined are substituted into formula (20), where λ may be 10⁶And calculating the control increment from the k moment to the k +9 moment

Eighth, a matrix formed by the control variables u (k) to u (k +9) from the time k to the time k +9 is calculated according to the formula (10), and finally, the determined control variables are applied to the controlled system.

Optionally, in the seventh step, the control increment Δ u (k) at the time k at the current time may be determined according to the formula (20), and further, the optimal control variable u (k) at the time k may be determined; the value of k is updated by setting k to k +1, and the third to seventh steps in the above steps are repeated until the value of k reaches the end of the control time, for example, k to k + 9.

The method of model predictive control according to the embodiment of the present invention is described in detail above with reference to fig. 1 to 4, and the apparatus of model predictive control according to the embodiment of the present invention will be described below with reference to fig. 5.

Fig. 5 shows a schematic block diagram of the apparatus 200 for model predictive control according to an embodiment of the present invention, and optionally, various modules in the apparatus 200 for model predictive control may be integrated into one chip, for example, various modules in the apparatus 200 for model predictive control may be included on a neuromorphic computing chip. As shown in fig. 5, the apparatus 200 for model predictive control according to an embodiment of the present invention includes:

a first determining module 210, configured to determine a parameter variable θ (k) at a time k (k-1) according to at least one of parameter variables θ (k-1) to θ (k-q) of the prediction model at the time k-1, a state variable x (k) at the time k, and a control variable u (k-1) at the time k-1;

a second determining module 220, configured to determine, by using a single-layer recurrent neural network algorithm, a control increment Δ u (k) that meets the performance criterion of the prediction model according to the state variable x (k), the control variable u (k-1), and the parameter variable θ (k) determined by the first determining module;

a third determining module 230, configured to determine a control variable u (k) of the predictive model at the time k according to the control variable u (k-1) of the predictive model and the control increment Δ u (k) determined by the second determining module, where u (k) is u (k-1) + Δ u (k);

a control module 240, configured to perform model predictive control according to the control variable u (k) of the predictive model determined by the third determination module.

Therefore, the apparatus for model predictive control according to the embodiment of the present invention determines, by using a single-layer recurrent neural network algorithm, a control increment Δ u (k) that satisfies a performance index of a predictive model according to a state variable x (k) and a parameter variable θ (k) at a current time k and a control variable u (k-1) at a previous time k-1, where the sum of the control increment Δ u (k) and the control variable u (k-1) at the time k-1 is the control variable u (k) at the current time k, and finally performs model predictive control according to the control variable u (k). Therefore, the control variable at the current moment which is more optimized compared with the prior art can be obtained, the calculation efficiency can be improved, the accuracy of the performance index is theoretically ensured, the closed-loop control system is gradually stable, the whole model prediction control system runs highly autonomously, and the automatic operation is realized.

In an embodiment of the present invention, the first determining module 210 may determine the parameter variable θ (k) at the time k according to at least one of the parameter variables θ (k-1) to θ (k-q) of the prediction model at the time k-1 to the time k-q, the state variable x (k) at the time k, and the control variable u (k-1) at the time k-1. Specifically, the model of the controlled object can be expressed as shown in formula (1), wherein a state variable of the controlled object at the current time k and a control variable of the controlled object at the previous time k-1 can be obtained in real time through measurement; the parameter variable θ (k) may be determined by the first determining module 210 according to at least one of the parameter variables θ (k-1) to θ (k-q) of the prediction model from time k-1 to time k-q, the state variable x (k) at time k, and the control variable u (k-1) at time k-1, specifically, the parameter variable θ (k) may be determined by using the prior art, and the parameter variable θ (k) may also be determined by using a single hidden layer neural network in an embodiment of the present invention, which is not limited thereto.

The first determining module 210 may be a dedicated processor, and the processor may include a plurality of units, such as a matrix product unit, a matrix inversion unit, a random number generation unit, a nonlinear function mapping unit, a storage unit, etc., specifically, the operation of the processor may include two modes, an offline training mode is mainly used for determining the configuration and the functional relationship of each unit in the processor, such as determining a model function θ (α) of the hidden layer neural network, and an online prediction mode is mainly used for determining corresponding output data through certain input data according to the offline training result, such as parameter variables (θ k) for determining k time, but the present invention is not limited thereto.

In the embodiment of the present invention, first, a model function θ (α) of the single hidden layer neural network may be determined by the first determining module 210, and specifically, an input parameter α (k) may be defined by formula (2), that is, for a parameter variable θ (k) at the current time, it may be represented as a function F (α (k)) of input parameters α (k), and since an input of the function is α (k), an output is a parameter variable θ (k), that is, it may be represented as a model function θ (α), where the input parameter α (k) satisfies formula (3), where x (k) is a state variable at the current time k, u' (k) is a predicted quantity of a control variable at the current time, that is, a predicted control variable, and the parameter variables from k-1 to k-q are θ (k-1) to θ (k-q), where q is a time constant, and may be defined by a user.

Specifically, the model function of the single hidden layer neural network can be determined by the following method in the offline training mode through the first determining module 210Firstly, the controlled object is analyzed off-line, and two groups of data theta (theta) (theta is a specific form of the number theta (α)) can be obtained₁，…,θ_s]And α ═ α₁，…,α_s]Where s is the number of sample data, defined by the user, the greater the number of samples, the greater the accuracy, but the higher the sampling cost, so a reasonable number of samples can be determined empirically, hi addition, each α and θ here have a one-to-one correspondence, i.e., for each input α_iCorrespondingly, an output θ can be obtained_i。

As shown in fig. 2, a single hidden layer neural network is constructed. The number of neurons of an input layer of the single hidden layer neural network is n + m + pq, n is the dimension of a state variable x (k), and m is the dimension of a control variable u (k); the number of neurons in an output layer is p, and p is the dimension of theta (k); the number of hidden layer neurons is L, and the value of L can be defined by a user; the hidden layer neuron excitation function is g (·), which can be determined by empirical values; the weight vector from the ith input layer to the hidden layer is w_iThe bias vector of the neuron is b_i，w_iAnd b_iCan be randomly generated.

Input parameter α ═ α in the sample₁，…,α_s]Substituting into formula (4), obtaining neuron matrix H. Obtaining matrix H and output theta in s samples ═ theta₁，…,θ_s]Substituting into formula (5) to obtain the weight parameters β of the neuron element of the single hidden layer neural network connected with the output layer, it can be determined that the model function θ (α) of the single hidden layer neural network after training is expressed as formula (6), wherein β_iRow i of the matrix of weight parameters β.

In the embodiment of the present invention, after the first determining module 210 determines the parameter variable θ (k) at time k, the parameter variable x (k +1) at time k +1 may be substituted into formula (1), and then the state variable x (k +1) at time k +1 may be determined, and then the parameter variable θ (k +1) at time k +1 may be determined according to the predicted control variable u '(k +1) at time k +1, and so on, and for determining the parameter variable θ (k + N) at any time k + N, the state variable x (k + N) at time k + N may be obtained by formula (7) according to the parameter variable θ (k) at time k and the predicted control variable u' (k + N-1) at time k + N-1, where the formula (7) is a modified form of formula (1) at time k + N, and a (θ (·)) is a first reference function related to θ (·), b (theta (-) is a second reference function with respect to theta (-) and N is a positive integer.

For the determined state variable x (k + N) at the time k + N and the predicted controlled variable u (k + N) at the time k + N, the input parameter α (k + N) can be similarly determined by equation (3) as shown in equation (8), and the parameter variable θ (k + N) at the time k + N can be obtained by substituting the input parameter α (k + N) into equation (6).

In the embodiment of the present invention, the second determining module 220 determines the control increment Δ u (k) satisfying the performance index of the prediction model according to the state variable x (k), the control variable u (k-1) and the parameter variable θ (k) of the first determining module 210 by a single-layer recurrent neural network algorithm. Optionally, the second determining module 220 may also be a recurrent neural network module, and may be composed of a special processor, and the processor may include a plurality of units, such as a matrix product unit, a matrix summation unit, a max function operation unit, and a random number generation unit.

Specifically, for the controlled system represented by formula (1), the second determining module 220 may define several parameters from time k to time k + N, as shown by formula (9), where the matrix x (k) is a matrix formed by state variables x (k +1) to x (k + N) from time k +1 to time k + N; the matrix u (k) is a matrix formed by control variables u (k) to u (k + N-1) from the time k to the time k + N-1; the matrix Δ u (k) is a matrix formed by the control increments Δ u (k) to Δ u (k + N-1) from the time k to the time k + N-1, and can be expressed as shown in the formula (10) for any one control increment Δ u (k + j). From equation (9) and equation (10), equation (1) can be expressed as shown in equation (11), where matrices S, V and M are expressed as shown in equation (12), respectively, where a (θ (-)) is a first reference function with respect to θ (-) and B (θ (-) is a second reference function with respect to θ (-) and is related to the controlled object; θ (-) can be a parameter variable at each time determined by the first determination module 210.

In an embodiment of the present invention, the performance index of MPC is expressed as shown in equation (13), where Q and R are arbitrary positive definite diagonal matrices, which can be selected by the user, and P satisfies inequality (14), where K is an auxiliary variable.

The constrained optimization problem of the performance index of the controlled object can be obtained by substituting the formula (11) into the formula (13), and can be represented as a formula (15), wherein each parameter also satisfies a formula (16), wherein the matrix is formed by the last n rows of S, V and M, respectively, n is the dimension of the state variable x (k), the maximum value and the minimum value of the control variable representing the prediction model, the maximum value and the minimum value of the state variable representing the prediction model, and the maximum value and the minimum value of the control increment representing the prediction model, and is a unit matrix of n x n.

Several matrix forms are defined as in equation (17), where for each row an m x N row matrix is defined, and for each row an m x N row matrix is defined.

The performance index as shown in equation (15) can be expressed as shown in equation (18) according to equation (17), and the corresponding equation (17) can be expressed as shown in equation (19).

In the embodiment of the present invention, the second determining module 220 may solve the constrained optimization problem online by designing a single-layer recurrent neural network, and the model and the self-learning method of the neural network may be defined by formula (20), that is, determining the control increment from time k to time k + N-1 in formula (9) according to formula (20), where λ is a sufficiently large positive real number, and a specific value thereof may be defined by a user. Through an optimization theory and a neurodynamics related theory, the neural network can be converged to a global optimal solution of a corresponding constraint optimization problem from any initial state.

In the embodiment of the present invention, the third determining module 230 determines the controlled variable u (k) of the predictive model at the time k according to the controlled variable u (k-1) and the control increment Δ u (k) of the predictive model, wherein u (k) is u (k-1) + Δ u (k). Specifically, for the control increment from the time k to the time k + N-1 determined in the second determining module 220, for example, for the control increment Δ u (k) at the time k, since the formula (9) is satisfied, the determined control increment Δ u (k) is summed with the obtained control variable u (k-1) at the time k-1 at the previous time, so that the control variable u (k) at the current time can be obtained, and so on, the third determining module 230 may calculate to obtain the control increment for the time k + N-1, and sum the control increment with the obtained control variable u (k + N-2) at the time k + N-2 at the previous time k + N-1, so that the control variable u (k + N-1) at the time k + N-1 can be obtained, and the present invention is not limited thereto.

In the embodiment of the present invention, the control module 240 performs model predictive control according to the control variable u (k) of the predictive model determined by the third determination module 230.

It should be understood that the apparatus 200 for model predictive control according to the embodiment of the present invention may correspond to the method 100 for performing model predictive control according to the embodiment of the present invention, and the above and other operations and/or functions of each module in the apparatus 200 for model predictive control are respectively for implementing corresponding processes of each method in fig. 1 to 2, and are not repeated herein for brevity.

As shown in fig. 6, an embodiment of the present invention further provides an apparatus 300 for model predictive control, which includes a processor 310, a memory 320, and a bus system 330. Wherein, the processor 310 and the memory 320 are connected by a bus system 330, the memory 320 is used for storing instructions, and the processor 310 is used for executing the instructions stored by the memory 320. The memory 320 stores program code, and the processor 310 may call the program code stored in the memory 320 to perform the following operations: determining a parameter variable theta (k) at the k moment according to at least one of parameter variables theta (k-1) to theta (k-q) of the prediction model at the k-1 moment to the k-q moment, a state variable x (k) at the k moment and a control variable u (k-1) at the k-1 moment; determining a control increment delta u (k) meeting the performance index of the prediction model according to the state variable x (k), the control variable u (k-1) and the parameter variable theta (k) by a single-layer recurrent neural network algorithm; determining a control variable u (k) of the predictive model at the time k according to the control variable u (k-1) and the control increment Δ u (k) of the predictive model, wherein u (k) is u (k-1) + Δ u (k); and performing model predictive control according to the control variable u (k) of the predictive model.

It should be understood that, in the embodiment of the present invention, the processor 310 may be a Central Processing Unit (CPU), and the processor 310 may also be other general-purpose processors, Digital Signal Processors (DSPs), Application Specific Integrated Circuits (ASICs), Field Programmable Gate Arrays (FPGAs) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, or the like. A general purpose processor may be a microprocessor or the processor may be any conventional processor or the like.

The memory 320 may include both read-only memory and random access memory and provides instructions and data to the processor 310. A portion of memory 320 may also include non-volatile random access memory. For example, the memory 320 may also store device type information.

The bus system 330 may include a power bus, a control bus, a status signal bus, and the like, in addition to a data bus. For clarity of illustration, however, the various buses are labeled in the figure as bus system 330.

In implementation, the steps of the above method may be performed by integrated logic circuits of hardware or instructions in the form of software in the processor 310. The steps of a method disclosed in connection with the embodiments of the present invention may be directly implemented by a hardware processor, or may be implemented by a combination of hardware and software modules in the processor. The software module may be located in ram, flash memory, rom, prom, or eprom, registers, etc. storage media as is well known in the art. The storage medium is located in the memory 320, and the processor 310 reads the information in the memory 320 and completes the steps of the method in combination with the hardware. To avoid repetition, it is not described in detail here.

Optionally, as an embodiment, the processor 310 may call the program code stored in the memory 320 to determine a model function θ (α) of the single hidden layer neural network, determine an input parameter α (k) ═ x (k); u '(k); θ (k-1); θ (k-q) ], where q is an integer, 1 ≦ q < k, based on the state variables x (k) of the prediction model, the predicted control variables u' (k) at the time k, and the parameter variables θ (k-1) through θ (k-q) at the time k-1 through the time k-q, and substitute the input parameter α (k) into the model function θ (α) to calculate the parameter variable θ (k) at the time k.

Optionally, as an embodiment, the processor 310 may call the program code stored in the memory 320 to determine the state variable x (k + N) of the prediction model at the time k + N according to the parameter variable θ (k) at the time k, the state variable x (k) and the predicted control variable u ' (k + N-1) at the time k + N, where a (θ (-)) is a first reference function with respect to θ (-) and B (θ (-)) is a second reference function with respect to θ (-) and N is a time step and N is a positive integer, by equation (7), determine the input parameter α (k + N) [ x (k + N) ], determine the predicted control variable u ' (k + N) at the time k + N and the parameter variables θ (k + N-1) to θ (k + N-q) from the state variable x (k + N), the predicted control variable u ' (k + N) at the time k + N-1) to the time k + N-q, and substitute the input parameter k + N (k + N-1) into the parameter (k + N-N k + N-q, where k + N-1 k-q is an input parameter α, where k + N-N, N-q is an input parameter (k + N) input parameter α).

Alternatively, the processor may, as an embodiment,processor 310 may call program code stored in memory 320 to determine s sets of input data α ═ α₁，…,α_s]And corresponding s sets of output data θ ═ θ₁，…,θ_s](ii) a Constructing the single hidden layer neural network, wherein the number of input layer neurons of the single hidden layer neural network is n + m + pq, the number of hidden layer neurons is L, the number of output layer neurons is p, a hidden layer neuron excitation function is g (·), and a weight vector from the ith input layer to the hidden layer is w_iThe bias vector of the neuron is b_iWhere n is the dimension of the state variable x (k) and m is the dimension of the control variable u (k), the input data α being [ α ] according to the single hidden layer neural network₁，…,α_s]And the output data theta ═ theta₁，…,θ_s]Determining the weight parameter β ═ H of the connection between the neuron of the single hidden layer neural network and the output layer^T(I+HH^T)^-1[θ₁,...,θ_s]Where H satisfies equation (4), determining the model function θ (α) is shown in equation (5), where β_iLine i of the weight parameter β.

Alternatively, as an embodiment, the processor 310 may call the program code stored in the memory 320 to perform the following operations: determining, by the single-layer recurrent neural network algorithm, the control increment Δ u (k) according to the following equation:

wherein the content of the first and second substances,

a (theta (-) is a first reference function about theta (-) and B (theta (-)) is a second reference function about theta (-) and a matrix formed by the last n rows of S, V and M, respectively, n is the dimension of the state variable x (k) [ -u/]_min+u(k-1)]For each row is-u_minM-row matrix of + u (k-1), [ u ] 1_max-u(k-1)]For each row is u_maxAn m-row matrix of u (k-1), m being the dimension of the control variable u (k), λ being a positive real number, u_maxAnd u_minMaximum and minimum values of control variables, x, representing the predictive model_maxAnd x_minRepresenting the maximum value and the minimum value of the state variable of the prediction model, Q and R are any positive definite diagonal matrix, and P satisfies the following inequality:

Q+K^TRK+(A(θ(k+1))+B(θ(k+1))K)^TP(A(θ(k+1))+B(θ(k+1))K)-P≤0

wherein P >0 and K is an auxiliary variable.

Alternatively, as an embodiment, the processor 310 may call the program code stored in the memory 320 to perform the following operations: determining, by the single-layer recurrent neural network algorithm, a control increment from the time k to the time k + N-1 according to formula (20), wherein matrices S, V and M satisfy formula (12), respectively, matrices W, p, E, and B satisfy formula (17), respectively, Δ u (k + j) -u (k + j-1) ], 0 ≦ j ≦ N, a (θ (-) is a first reference function for θ (-) and B (θ (-)) is a second reference function for θ (-) and a matrix of the last N rows S, V and M, respectively, N is a dimension of the state variable (x k), M × N row matrix for each row, M is a dimension of the control variable u (k), N is a time step, λ is a positive real number, and a maximum value and a minimum value of the control variable representing the predictive model, and expressing the maximum value and the minimum value of the state variable of the prediction model, Q and R are any positive definite diagonal matrix, P satisfies inequality (14), and K is an auxiliary variable.

Alternatively, as an embodiment, the processor 310 may call the program code stored in the memory 320 to perform the following operations: and determining the control variable from the k moment to the k + N-1 moment according to the control increment from the k moment to the k + N-1 moment and the control variable from the k-1 moment to the k + N-2 moment, wherein model prediction control is carried out according to the control variable from the k moment to the k + N-1 moment.

It should be understood that the apparatus 300 for model predictive control according to the embodiment of the present invention may correspond to the apparatus 200 for model predictive control according to the embodiment of the present invention, and may correspond to a corresponding subject executing the method 100 according to the embodiment of the present invention, and the above and other operations and/or functions of each module in the apparatus 300 for model predictive control are not repeated herein for brevity in order to implement the corresponding flow of each method in fig. 1 to 2, respectively.

Those of ordinary skill in the art will appreciate that the various illustrative elements and algorithm steps described in connection with the embodiments disclosed herein may be implemented as electronic hardware or combinations of computer software and electronic hardware. Whether such functionality is implemented as hardware or software depends upon the particular application and design constraints imposed on the implementation. Skilled artisans may implement the described functionality in varying ways for each particular application, but such implementation decisions should not be interpreted as causing a departure from the scope of the present invention.

It is clear to those skilled in the art that, for convenience and brevity of description, the specific working processes of the above-described systems, apparatuses and units may refer to the corresponding processes in the foregoing method embodiments, and are not described herein again.

In the several embodiments provided in the present application, it should be understood that the disclosed system, apparatus and method may be implemented in other ways. For example, the above-described apparatus embodiments are merely illustrative, and for example, the division of the units is only one logical division, and other divisions may be realized in practice, for example, a plurality of units or components may be combined or integrated into another system, or some features may be omitted, or not executed. In addition, the shown or discussed mutual coupling or direct coupling or communication connection may be an indirect coupling or communication connection through some interfaces, devices or units, and may be in an electrical, mechanical or other form.

The units described as separate parts may or may not be physically separate, and parts displayed as units may or may not be physical units, may be located in one place, or may be distributed on a plurality of network units. Some or all of the units can be selected according to actual needs to achieve the purpose of the solution of the embodiment.

In addition, functional units in the embodiments of the present invention may be integrated into one processing unit, or each unit may exist alone physically, or two or more units are integrated into one unit.

The functions, if implemented in the form of software functional units and sold or used as a stand-alone product, may be stored in a computer readable storage medium. Based on such understanding, the technical solution of the present invention may be embodied in the form of a software product, which is stored in a storage medium and includes instructions for causing a computer device (which may be a personal computer, a server, or a network device) to execute all or part of the steps of the method according to the embodiments of the present invention. And the aforementioned storage medium includes: a U-disk, a removable hard disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), a magnetic disk or an optical disk, and other various media capable of storing program codes.

The above description is only for the specific embodiments of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art can easily conceive of the changes or substitutions within the technical scope of the present invention, and all the changes or substitutions should be covered within the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims

A method of model predictive control, the method comprising:

determining a parameter variable theta (k) at the k moment according to at least one of parameter variables theta (k-1) to theta (k-q) of a prediction model at the k-1 moment to the k-q moment, a state variable x (k) at the k moment and a control variable u (k-1) at the k-1 moment;

solving a quadratic programming problem on line by a single-layer recurrent neural network algorithm, and determining a control increment delta u (k) meeting the performance index of the prediction model according to the state variable x (k), the control variable u (k-1) and the parameter variable theta (k);

determining a control variable u (k) of the predictive model at the time k according to the control variable u (k-1) and the control increment Δ u (k) of the predictive model, wherein u (k) is u (k-1) + Δ u (k);

and performing model predictive control according to the control variables u (k) of the predictive model.
The method of claim 1, wherein determining the parameter variable θ (k) at time k according to at least one of the parameter variables θ (k-1) to θ (k-q) of the predictive model at time k-1 to time k-q, the state variable x (k) at time k, and the control variable u (k-1) at time k-1 comprises:

determining a model function θ (α) for the single hidden layer neural network;

determining an input parameter α (k) ═ x (k); u '(k); θ (k-1); θ (k-q) ], where q is an integer, 1 ≦ q < k, based on the state variables x (k), the predictive control variables u' (k) at the time k, and the parameter variables θ (k-1) through θ (k-q) at the time k-1 through the time k-q of the predictive model;

and substituting the input parameters α (k) into the model function theta (α) to calculate the parameter variable theta (k) at the k moment.
The method of claim 2, wherein determining the model function θ (α) for the single hidden layer neural network comprises:

determining s sets of input data α ═ α₁，…,α_s]And corresponding s sets of output data θ ═ θ₁，…,θ_s]；

Constructing the single hidden layer neural network, wherein the number of input layer neurons of the single hidden layer neural network is n + m + pq, the number of hidden layer neurons is L, the number of output layer neurons is p, a hidden layer neuron excitation function is g (·), and a weight vector from the ith input layer to the hidden layer is w_iThe bias vector of the neuron is b_iWherein n is the dimension of the state variable x (k) and m is the dimension of the control variable u (k);

the input data α ═ α according to the single hidden layer neural network₁，…,α_s]And said output data θ ═ θ₁，…,θ_s]Determining the weight parameter β ═ H of the connection between the neuron of the single hidden layer neural network and the output layer^T(I+HH^T)^-1[θ₁,...,θ_s]Wherein:

determining the model function θ (α):

wherein, β_iRow i of the weight parameter β.
A method according to claim 2 or 3, characterized in that the method further comprises:

determining the state variable x (k + N) of the prediction model at the time k + N according to the parameter variable theta (k) at the time k, the state variable x (k), and the predictive control variable u' (k + N-1) at the time k + N-1 by the following formula:

x(k+N)＝A(θ(k+N-1))x(k+N-1))+B(θ(k+N-1))u'(k+N-1))

where A (θ (-)) is a first reference function with respect to θ (-) and B (θ (-)) is a second reference function with respect to θ (-) with N being a time step and N being a positive integer;

determining an input parameter α (k + N) ═ x (k + N) [ [ x (k + N) ]u '(k + N) ] [ theta (k + N ] [ theta (k + N) ], theta (k + N-1) ], theta (k + N-q) ], wherein q is an integer, and 1 is less than or equal to q < k, according to the state variable x (k + N), a predictive control variable u' (k + N) at the time k + N, and parameter variables theta (k + N-1) to theta (k + N-q) at the time k +;

and substituting the input parameters α (k + N) into the model function theta (α) to calculate the parameter variable theta (k + N) at the k + N moment.
The method according to any one of claims 1 to 4, wherein the solving of the quadratic programming problem on-line by a single-layer recurrent neural network algorithm, determining the control increment Δ u (k) satisfying the prediction model performance index according to the state variable x (k), the control variable u (k-1) and the parameter variable θ (k), comprises:

determining, by the single-layer recurrent neural network algorithm, the control increment Δ u (k) according to the following equation:

wherein the content of the first and second substances,

a (theta (-) is a first reference function with respect to theta (-) and B (theta (-)) is a second reference function with respect to theta (-) and a matrix of the last n rows S, V and M, respectively, n being the dimension, -u, of the state variable x (k)_min+ u (k-1) is-u for each row_minM-row matrix of + u (k-1), u_max-u (k-1) is u for each row_max-a matrix of m rows of u (k-1), m being the dimension of the control variable u (k), λ being a positive real number, u_maxAnd u_minMaximum and minimum values, x, of control variables representing said predictive model_maxAnd x_minRepresenting the maximum and minimum values of the state variables of the prediction model, Q and R being any positive definite diagonal matrix, P satisfying the following inequality:

Q+K^TRK+(A(θ(k+1))+B(θ(k+1))K)^TP(A(θ(k+1))+B(θ(k+1))K)-P≤0

wherein P >0 and K is an auxiliary variable.
The method according to claim 3 or 4, characterized in that the method further comprises:

solving a quadratic programming problem on line through the single-layer recurrent neural network algorithm, and determining the control increment from the k moment to the k + N-1 moment according to the following formula

Wherein the content of the first and second substances,

Δ u (k + j) ═ u (k + j) -u (k + j-1) ], 0 ≦ j ≦ N, a (θ (·)) is a first reference function with respect to θ (·), B (θ (·)) is a second reference function with respect to θ (·), and matrices formed by the last N rows of S, V and M, respectively, N is a dimension of the state variable x (k), is a matrix of M × N rows for each row, M is a dimension of the control variable u (k), N is a time step, λ is a positive real number, represents a maximum and a minimum of the control variable of the prediction model, and represents a maximum and a minimum of the state variable of the prediction model, Q and R are arbitrary positive diagonal matrices, P satisfies the following inequality:

Q+K^TRK+(A(θ(k+N))+B(θ(k+N))K)^TP(A(θ(k+N))+B(θ(k+N))K)-P≤0

wherein P >0 and K is an auxiliary variable.
The method of claim 6, further comprising:

determining the control variables from the k moment to the k + N-1 moment according to the control increment from the k moment to the k + N-1 moment and the control variables from the k-1 moment to the k + N-2 moment,

and performing model predictive control according to the control variables from the time k to the time k + N-1.
An apparatus for model predictive control, the apparatus comprising:

a first determining module, which is used for determining a parameter variable theta (k) at the k moment according to at least one of parameter variables theta (k-1) to theta (k-q) of a prediction model at the k-1 moment to the k-q moment, a state variable x (k) at the k moment and a control variable u (k-1) at the k-1 moment;

the second determining module is used for solving a quadratic programming problem on line through a single-layer recurrent neural network algorithm, and determining a control increment delta u (k) meeting the performance index of the prediction model according to the state variable x (k), the control variable u (k-1) and the parameter variable theta (k) determined by the first determining module;

a third determining module, configured to determine, according to the control variable u (k-1) of the prediction model and the control increment Δ u (k) determined by the second determining module, a control variable u (k) of the prediction model at the time k, where u (k) is u (k-1) + Δ u (k);

and the control module is used for carrying out model prediction control according to the control variable u (k) of the prediction model determined by the third determination module.
The apparatus of claim 8, wherein the first determining module is specifically configured to:

determining a model function θ (α) for the single hidden layer neural network;

determining an input parameter α (k) ═ x (k); u '(k); θ (k-1); θ (k-q) ], where q is an integer, 1 ≦ q < k, based on the state variables x (k), the predictive control variables u' (k) at the time k, and the parameter variables θ (k-1) through θ (k-q) at the time k-1 through the time k-q of the predictive model;

and substituting the input parameters α (k) into the model function theta (α) to calculate the parameter variable theta (k) at the k moment.
The apparatus of claim 9, wherein the first determining module is specifically configured to:

determining s sets of input data α ═ α₁，…,α_s]And corresponding s sets of output data θ ═ θ₁，…,θ_s]；

Constructing the single hidden layer neural network, wherein the number of input layer neurons of the single hidden layer neural network is n + m + pq, the number of hidden layer neurons is L, the number of output layer neurons is p, a hidden layer neuron excitation function is g (·), and a weight vector from the ith input layer to the hidden layer is w_iThe bias vector of the neuron is b_iWherein n is the dimension of the state variable x (k) and m is the dimension of the control variable u (k);

the input data α ═ α according to the single hidden layer neural network₁，…,α_s]And said output data θ ═ θ₁，…,θ_s]Determining the weight parameter β ═ H of the connection between the neuron of the single hidden layer neural network and the output layer^T(I+HH^T)^-1[θ₁,...,θ_s]Wherein:

determining the model function θ (α):

wherein, β_iRow i of the weight parameter β.
The apparatus according to claim 9 or 10, wherein the first determining module is specifically configured to:

determining the state variable x (k + N) of the prediction model at the time k + N according to the parameter variable theta (k) at the time k, the state variable x (k), and the predictive control variable u' (k + N-1) at the time k + N-1 by the following formula:

x(k+N)＝A(θ(k+N-1))x(k+N-1))+B(θ(k+N-1))u'(k+N-1))

where A (θ (-)) is a first reference function with respect to θ (-) and B (θ (-)) is a second reference function with respect to θ (-) with N being a time step and N being a positive integer;

determining an input parameter α (k + N) ═ x (k + N) [ [ x (k + N) ]u '(k + N) ] [ theta (k + N ] [ theta (k + N) ], theta (k + N-1) ], theta (k + N-q) ], wherein q is an integer, and 1 is less than or equal to q < k, according to the state variable x (k + N), a predictive control variable u' (k + N) at the time k + N, and parameter variables theta (k + N-1) to theta (k + N-q) at the time k +;

and substituting the input parameters α (k + N) into the model function theta (α) to calculate the parameter variable theta (k + N) at the k + N moment.
The apparatus according to any one of claims 8 to 11, wherein the second determining module is specifically configured to:

determining, by the single-layer recurrent neural network algorithm, the control increment Δ u (k) according to the following equation:

wherein the content of the first and second substances,

a (theta (-) is a first reference function related to theta (-) and B (theta (-)) is a second reference function related to theta (-) and a matrix formed by the last n rows of S, V and M respectively, n is the state variableDimension of x (k) [ -u [)_min+u(k-1)]For each row is-u_minM-row matrix of + u (k-1), [ u ] 1_max-u(k-1)]For each row is u_max-a matrix of m rows of u (k-1), m being the dimension of the control variable u (k), λ being a positive real number, u_maxAnd u_minMaximum and minimum values, x, of control variables representing said predictive model_maxAnd x_minRepresenting the maximum and minimum values of the state variables of the prediction model, Q and R being any positive definite diagonal matrix, P satisfying the following inequality:

Q+K^TRK+(A(θ(k+1))+B(θ(k+1))K)^TP(A(θ(k+1))+B(θ(k+1))K)-P≤0

wherein P >0 and K is an auxiliary variable.
The apparatus of claim 10 or 11, wherein the second determining module is further configured to:

determining the control increment from the k time to the k + N-1 time according to the following formula by the single-layer recurrent neural network algorithm

Wherein the content of the first and second substances,

Δ u (k + j) ═ u (k + j) -u (k + j-1) ], 0 ≦ j ≦ N, a (θ (·)) is a first reference function with respect to θ (·), B (θ (·)) is a second reference function with respect to θ (·), and a matrix of the last N rows of S, V and M, respectively, N is a dimension of the state variable x (k), an M × N row matrix for each row, M is a dimension of the control variable u (k), N is a time step, λ is a positive real number, and control variable maximum and minimum values representing the prediction model, and state variable maximum and minimum values representing the prediction model, Q and R are arbitrary positive diagonal matrices, P satisfies the following inequality:

Q+K^TRK+(A(θ(k+N))+B(θ(k+N))K)^TP(A(θ(k+N))+B(θ(k+N))K)-P≤0

wherein P >0 and K is an auxiliary variable.
The apparatus of claim 13, wherein the third determining module is further configured to:

determining the control variable from the k moment to the k + N-1 moment according to the control increment from the k moment to the k + N-1 moment and the control variable from the k-1 moment to the k + N-2 moment

And performing model predictive control according to the control variables from the time k to the time k + N-1.