WO2017024583A1 - 模型预测控制的方法和装置 - Google Patents
模型预测控制的方法和装置 Download PDFInfo
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- the present invention relates to the field of information technology, and in particular, to a method and apparatus for model predictive control.
- Model Predictive Control is a control strategy with limited time-domain multi-step prediction, rolling optimization and feedback correction. It is widely used in many fields such as networked control and resource scheduling management.
- the core idea of MPC is to predict the state of the next N finite moments of the controlled system at each sampling moment, and then solve the finite time domain optimal control problem to obtain the optimal control signal at the current moment.
- J(k) is the performance index of the control system
- Q and R are the coefficient matrix, which can be set to the corresponding matrix according to the actual application
- F(x(k+N)) is about the state variable x(k+N) Function, the function can be set according to the actual application
- u max and u min are the upper and lower bounds of the constraint of the control input, respectively
- x max and x min are the upper and lower bounds of the constraint of the system state, respectively
- N is the prediction step size.
- the biggest problem with this technology is the conservative nature of its calculations. Designing optimal control signals under the MPC framework, the goal is to achieve the best performance of system-specific performance indicators.
- the existing minimum-maximum (min-max) optimization scheme considers the worst case that the system may appear, but for the controlled object, its manifestation at each moment is certain, and often does not present the worst. situation. In this case, optimizing the worst case performance indicators undoubtedly sacrifices overall control performance.
- the acquisition of the MPC optimal control signal is based on the optimization of the future prediction state of the system. If there is a large error between the model f(x, u) of the controlled system and the actual controlled object, then the optimal control is obtained. It is difficult to obtain a satisfactory control effect with the signal.
- the invention provides a method and a device for model predictive control, which can improve the calculation efficiency and ensure the reliability of the performance index of the model predictive control.
- a method for model predictive control comprising: a state of a parameter variable ⁇ (k-1) to ⁇ (kq) at a time k1 from k-1 to a time at a time k Determining at least one of the variable x(k) and the control variable u(k-1) at the k-1 time, the parameter variable ⁇ (k) at the k-time; solving the quadratic solution online by the single-layer recurrent neural network algorithm a planning problem, based on the state variable x(k), the control variable u(k-1), and the parameter variable ⁇ (k), determining a control increment ⁇ u(k) that satisfies the performance model of the prediction model;
- the method further includes: the parameter variable ⁇ (k) according to the k time, the state variable x(k), and k+
- the predicted control variable u'(k+N-1) at time N-1 is determined by the following formula to determine the state variable x(k+N) at k+N:
- x(k+N) A( ⁇ (k+N-1))x(k+N-1))+B( ⁇ (k+N-1))u'(k+N-1))
- A( ⁇ ( ⁇ )) is the first reference function for ⁇ ( ⁇ )
- B( ⁇ ( ⁇ )) is the second reference function for ⁇ ( ⁇ )
- N is the time step, and N is a positive integer
- the quadratic programming problem is solved online by a single layer recursive neural network algorithm, according to the state variable x(k), the control variable u (k-1) and the parameter variable ⁇ (k), determining a control increment ⁇ u(k) that satisfies the performance model of the prediction model, including: determining, by the single layer recursive neural network algorithm, the control increment according to the following formula ⁇ u(k):
- A( ⁇ ( ⁇ )) is the first reference function for ⁇ ( ⁇ ), and B( ⁇ ( ⁇ )) is the second reference function for ⁇ ( ⁇ ), with The matrix consisting of the last n rows of S, V, and M, where n is the dimension of the state variable x(k), and -u min +u(k-1) is -u min +u(k- for each row 1) of the m rows of the matrix, u max -u (k-1 ) for the dimension control variable u (k) for each row are u max -u (k-1) of the m rows of the matrix, m, ⁇ is a positive Real numbers, u max and u min represent the maximum and minimum values of the control variables of the prediction model, x max and x min represent the maximum and minimum values of the state variables of the prediction model, Q and R are arbitrary positive definite diagonal matrices, and P satisfies The following inequality:
- K is an auxiliary variable.
- the method further includes: solving the quadratic programming problem online by using the single layer recursive neural network algorithm, and determining the k time according to the following formula Control increment to k+N-1
- A( ⁇ ( ⁇ )) is the first reference function for ⁇ ( ⁇ )
- B ( ⁇ ( ⁇ )) is the second reference function for ⁇ ( ⁇ )
- n is the dimension of the state variable x(k)
- n is the dimension of the state variable x(k)
- m is the dimension of the control variable u(k)
- N is the time step
- ⁇ is the positive real number.
- K is an auxiliary variable.
- the method further includes: the control increment according to the k time to the k+N-1 time And the control variable from the time k-1 to the time k+N-2 Determining the control variable from the time k to the time k+N-1 among them, According to the control variable from the k time to the k+N-1 time Perform model prediction control.
- an apparatus for model predictive control comprising: a first determining module for parameter variables ⁇ (k-1) to ⁇ according to a prediction model at time k-1 to kq ( Kq), at least one of the state variable x(k) at time k and the control variable u(k-1) at the time k-1, determining a parameter variable ⁇ (k) at the k-time; second determination a module for solving a quadratic programming problem online by a single-layer recurrent neural network algorithm, according to the state variable x(k), the control variable u(k-1), and the parameter variable ⁇ (k) determined by the first determining module Determining a control increment ⁇ u(k) that satisfies the performance model of the predictive model; a third determining module, configured to use the control variable u(k-1) of the predictive model and the control increase determined by the second determining module a quantity ⁇ u(k) that determines a control variable u(k) of
- the first determining module is specifically configured to: according to the parameter variable ⁇ (k) at the k time, the state variable x(k) And the predictive control variable u'(k+N-1) at time k+N-1, the state variable x(k+N) of the predictive model at k+N is determined by the following formula:
- x(k+N) A( ⁇ (k+N-1))x(k+N-1))+B( ⁇ (k+N-1))u'(k+N-1))
- A( ⁇ ( ⁇ )) is the first reference function for ⁇ ( ⁇ )
- B( ⁇ ( ⁇ )) is the second reference function for ⁇ ( ⁇ )
- N is the time step, and N is a positive integer
- the second determining module is specifically configured to: according to the single layer recursive neural network algorithm, according to the following formula The control increment ⁇ u(k) is determined:
- A( ⁇ ( ⁇ )) is the first reference function for ⁇ ( ⁇ ), and B( ⁇ ( ⁇ )) is the second reference function for ⁇ ( ⁇ ), with The matrix consisting of the last n rows of S, V, and M, where n is the dimension of the state variable x(k), and -u min +u(k-1) is -u min +u(k- for each row 1) of the m rows of the matrix, u max -u (k-1 ) for the dimension control variable u (k) for each row are u max -u (k-1) of the m rows of the matrix, m, ⁇ is a positive Real numbers, u max and u min represent the maximum and minimum values of the control variables of the prediction model, x max and x min represent the maximum and minimum values of the state variables of the prediction model, Q and R are arbitrary positive definite diagonal matrices, and P satisfies The following inequality:
- K is an auxiliary variable.
- the second determining module is further configured to: determine, by using the single layer recursive neural network algorithm, the k time to k according to the following formula +N-1 time control increment
- A( ⁇ ( ⁇ )) is the first reference function for ⁇ ( ⁇ )
- B ( ⁇ ( ⁇ )) is the second reference function for ⁇ ( ⁇ )
- n is the dimension of the state variable x(k)
- n is the dimension of the state variable x(k)
- m is the dimension of the control variable u(k)
- N is the time step
- ⁇ is the positive real number.
- K is an auxiliary variable.
- the third determining module is further configured to: according to the control increment of the k time to the k+N-1 time And the control variable from the time k-1 to the time k+N-2 Determining the control variable from the time k to the time k+N-1 among them, According to the control variable from the k time to the k+N-1 time Perform model prediction control.
- the method and apparatus for model predictive control according to the state variable x(k) and the parameter variable ⁇ (k) at the current time k, and the control variable u at the previous time k-1 (k-1), through the single-layer recurrent neural network algorithm, determine the control increment ⁇ u(k) that satisfies the performance index of the prediction model, the control increment ⁇ u(k) and the control variable u(k-1 at time k-1) The sum of the ) is the control variable u(k) at the current time k, and finally the model predictive control is performed based on the control variable u(k).
- FIG. 1 is a schematic flow chart of a method of model predictive control according to an embodiment of the present invention.
- FIG. 2 is a schematic diagram of a single hidden layer neural network structure in accordance with an embodiment of the present invention.
- FIG. 3 is a schematic illustration of control variable comparison of a mass spring system in accordance with an embodiment of the present invention.
- FIG. 4 is a schematic illustration of a state variable comparison of a mass spring system in accordance with an embodiment of the present invention.
- FIG. 5 is a schematic block diagram of an apparatus for model predictive control according to an embodiment of the present invention.
- FIG 6 is another schematic block diagram of an apparatus for model predictive control in accordance with an embodiment 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 present invention. As shown in FIG. 1, the method 100 includes:
- S140 Perform model prediction control according to the control variable u(k) of the prediction model.
- the state variable x(k) of the prediction model at time k and the control variable u(k-1) at time k-1 are acquired, according to the state variable x(k) and the control variable u(k-1), Determining the parameter variable ⁇ (k) at the time k, optionally, the parameter variable ⁇ (k) can be determined by training the model of the hidden layer neural network; by the single-layer recurrent neural network algorithm, according to the state variable x(k) ), the control variable u(k-1) and the parameter variable ⁇ (k), determine the control increment ⁇ u(k) that satisfies the performance index of the prediction model, the control increment ⁇ u(k) and the control variable at time k-1
- the sum of u(k-1) is the control variable u(k) at the current time k, and the model predictive control is performed by the control variable at the current time k.
- the method of the embodiment of the present invention may be implemented by using a neural network architecture, for example, the prediction process of determining the parameter variable ⁇ (k) in the method and the online optimization process of determining the control increment ⁇ u(k) may pass
- the neural network architecture is completed, and the neural network architecture can be completed by a neuromorphic computing chip, and the present invention is not limited thereto.
- the method for model predictive control is based on the state variable x(k) and the parameter variable ⁇ (k) at the current time k, and the control variable u(k-1) at the time k-1 at the previous time.
- the control increment ⁇ u(k) that satisfies the performance index of the prediction model is determined by a single-layer recurrent neural network algorithm, and the sum of the control increment ⁇ u(k) and the control variable u(k-1) at time k-1 is current
- the control variable u(k) at time k is finally subjected to model prediction control based on the control variable u(k).
- the model specifically represented by the controlled object may be expressed as a form of formula (1):
- x(k) is the state variable of the system at the current moment k, which can be obtained from the real-time measurement in the controlled process
- u(k) is the control variable of the system at the current moment k, that is, the control signal, which is currently unknown
- A( ⁇ ( ⁇ )) and B( ⁇ ( ⁇ )) are reference functions related to the parameter variable ⁇ (k) in the controlled process, which can be regarded as the form of the parameter matrix, and its specific form depends on the parameter variable ⁇ (k
- the value of ⁇ (k) is measurable in real time from the controlled process.
- the control problem has a known target output that is designed to approximate the actual output of the controlled process to the target output by designing u(k).
- typical use cases of the embodiments of the present invention include: resource management of the data center, automatic control of the robot, supply chain management of the semiconductor production, building energy-saving control, and drone flight control.
- a significant common feature of these use cases is that their control objectives are to achieve optimization of a performance metric describing the behavior of the global system, while constraints on physical conditions define the range of control actions that can be taken. To the extent practicable, there is always a control behavior that minimizes the performance metrics describing the global system. For example, for resource management in the data center, an important global performance indicator is the overall energy consumption of the system.
- the state variables of the predictive control may include the temperature, power consumption, or resource utilization of the data center, and the control signal may be It is a fan/air conditioner rotational speed, a CPU thread allocation command, etc., but the present invention is not limited thereto.
- the parameter variables ⁇ (k-1) to ⁇ (kq) at the time k1 from the time k1 at the time of the prediction model, the state variable x(k) at the time k, and the control at the time k-1 At least one of the variables u(k-1) determines the parameter variable ⁇ (k) at the time k.
- the model for the controlled object can be expressed as shown in the formula (1), wherein the state variable of the current time at the time k of the controlled object and the control variable at the time k-1 at the time k of the controlled object can be measured.
- the parameter variable ⁇ (k) can be based on the parameter variables ⁇ (k-1) to ⁇ (kq) of the prediction model at k-1 to kq, the state variable x(k) at time k, and At least one of the control variables u(k-1) at the k-1 time is determined.
- the parameter variable ⁇ (k) may be determined by using the prior art, or the single hidden layer nerve may be used in the embodiment of the present invention.
- the network determines the parameter variable ⁇ (k), and the present invention is not limited thereto.
- the parameter variable ⁇ (k) can be modeled and evaluated online by a single hidden layer neural network.
- Neural network is a computational model that simulates the behavioral characteristics of human brain structure and performs distributed parallel information processing. Neural networks rely on their learning algorithms to adjust the interconnections between a large number of their internal neurons to achieve specific computational goals.
- the model function ⁇ ( ⁇ ) of the single hidden layer neural network can be determined.
- an input parameter ⁇ (k) can be defined by the following formula (2):
- the parameter variable ⁇ (k) at the current time it can be expressed as a function F( ⁇ (k)) about the input parameter ⁇ (k). Since the input of the function is ⁇ (k), the output is the parameter variable ⁇ ( k), which can be expressed as a model function ⁇ ( ⁇ ), where the input parameter ⁇ (k) satisfies the following formula (3):
- x(k) is the state variable at the current moment k
- u'(k) is the predicted amount of the control variable at the current time, that is, the predictive control variable
- the parameter variable at time k-1 to kq is ⁇ (k- 1) to ⁇ (kq), where q is a time constant, which can be defined by the user.
- the specific form of the model function ⁇ ( ⁇ ) of the single hidden layer neural network can be determined by the following method.
- s is the number of sample data, which is defined by the user.
- each ⁇ and ⁇ here correspond one-to-one, that is, for each input ⁇ i , an output ⁇ i can be correspondingly obtained.
- a single hidden layer neural network is constructed.
- the number of input layer neurons in the single hidden layer neural network is n+m+pq, n is the dimension of the state variable x(k), m is the dimension of the control variable u(k); the number of neurons in the output layer is p,p
- the dimension of ⁇ (k); the number of hidden layer neurons is L, the value of L can be defined by the user; the excitation function of the hidden layer neurons is g( ⁇ ), and g( ⁇ ) can be determined by empirical values;
- the weight vector of the input layer to the hidden layer is w i
- the bias vector of the neuron is b i
- w i and b i can be randomly generated.
- ⁇ i is the ith row of the matrix of the weight parameter ⁇ .
- the input parameter ⁇ (k) defined by the formula (3) is input, and is substituted into the formula (6) to obtain the parameter variable ⁇ (k) at time k.
- the parameter variable ⁇ (k) at time k may be substituted into the formula (1), and the state variable x(k+1) at time k+1 may be determined, and then according to k+1.
- the predicted control variable u'(k+1) of the time can determine the parameter variable ⁇ (k+1) at time k+1, and so on, for determining the parameter variable ⁇ (k+N) at the time of k+N at any time.
- N is the prediction step size.
- x(k+N) A( ⁇ (k+N-1))x(k+N-1)+B( ⁇ (k+N-1))u'(k+N-1) (7)
- the formula (7) is a deformation form of the formula (1) at time k+N, A( ⁇ ( ⁇ )) is a first reference function with respect to ⁇ ( ⁇ ), and B( ⁇ ( ⁇ )) is about The second reference function of ⁇ ( ⁇ ), where N is a positive integer.
- ⁇ (k+N) [x(k+N);u'(k+N); ⁇ (k+N-1);...; ⁇ (k+N-q)] (8)
- the parameter variable ⁇ (k+N) at the time k+N can be obtained.
- the unknown parameter is modeled and estimated by using a single hidden layer neural network, and the model mismatch problem in the predictive control of the linear variable parameter system is better solved.
- the neural network has a simple structure and a fast training speed, avoids complicated iterative training of the traditional neural network, and improves the calculation efficiency.
- the matrix a matrix consisting of state variables x(k+1) to x(k+N) from time k+1 to k+N; matrix a matrix composed of control variables u(k) to u(k+N-1) from time k to k+N-1; matrix A matrix consisting of control increments ⁇ u(k) to ⁇ u(k+N-1) from time k to k+N-1, for any one of the control increments ⁇ u(k+j), can be expressed as a formula ( 10):
- A( ⁇ ( ⁇ )) is the first reference function for ⁇ ( ⁇ )
- B( ⁇ ( ⁇ )) is the second reference function for ⁇ ( ⁇ ), related to the controlled object
- ⁇ ( ⁇ ) It may be a parameter variable at each moment determined in S110.
- the performance index of the MPC is expressed as shown in the following formula (13):
- K is an auxiliary variable
- each parameter also satisfies the following formula (16):
- the neural network model and self-learning method can be defined by the following formula (20), that is, according to the following formula (20) Determine the control increment in time (from k) to k+N-1 in equation (9)
- ⁇ is a sufficiently large positive real number whose specific value can be defined by the user.
- the neural network can converge from any initial state to the global optimal solution corresponding to the constrained optimization problem.
- the control increment of time k to k+N-1 can be determined by the above formula (20).
- the recursive neural network is used to calculate the optimal control variable online, that is, the optimal control signal, and the calculation efficiency is high and the real-time performance is good.
- the number of neurons in the neural network and the learning algorithm are quantitatively and qualitatively given, and the implementation is simple and convenient, and no internal adjustment of internal parameters is required.
- the control increment for the time k to k+N-1 determined in S130 For example, for the control increment ⁇ u(k) at time k, since the formula (9) is satisfied, the determined control increment ⁇ u(k) and the obtained control variable u(k-1 at the previous time k-1) are obtained.
- control variable u(k+N-1) at the time k+N-1 and the state variable x(k+N-1) obtained in the real-time measurement are substituted into the formula (7),
- the state variable x(k+N) at the time k+N, and so on, obtains the state variable and the control variable at any time after the k time and the k time, and the present invention is not limited thereto.
- model prediction control is performed based on the control variable u(k) of the prediction model.
- the size of the sequence numbers of the above processes does not mean the order of execution, and the order of execution of each process should be determined by its function and internal logic, and should not be taken to the embodiments of the present invention.
- the implementation process constitutes any limitation.
- the method for model predictive control is based on the state variable x(k) and the parameter variable ⁇ (k) at the current time k, and the control variable u(k-1) at the time k-1 at the previous time.
- the control increment ⁇ u(k) that satisfies the performance index of the prediction model is determined by a single-layer recurrent neural network algorithm, and the sum of the control increment ⁇ u(k) and the control variable u(k-1) at time k-1 is current
- the control variable u(k) at time k is finally subjected to model prediction control based on the control variable u(k).
- equation (21) a form as shown in equation (21) can be written in the mass spring system, wherein the first reference function A ( ⁇ (k)) and the second
- the specific form of the reference function B is as shown in the following formula (22):
- the control variable may be an applied external force, but the invention is not limited thereto.
- the implementation process of the control method of the embodiment of the present invention on the mass spring system is as follows:
- the matrix a matrix consisting of state variables x(k+1) to x(k+20) from time k+1 to k+20; matrix a matrix consisting of control variables u(k) to u(k+19) from time k to time k+19; matrix A matrix composed of control increments ⁇ u(k) to ⁇ u(k+19) from time k to time k+19, for any one of the control increments ⁇ u(k+j), can be expressed as shown in equation (10) .
- a single hidden layer neural network is constructed to determine the parameter variable ⁇ (k).
- the input parameter ⁇ (k) is defined according to formula (3).
- ⁇ [ ⁇ 1 , ..., ⁇ 2000 ] specific values.
- the number of neurons in the input layer is 6; the number of hidden layers is set to 1000, which can be determined by the user. Meaning; the number of neurons in the output layer is 1.
- the weight vector w i of the input layer to the hidden layer is randomly generated, and the offset vector of the neuron is b i .
- the output data ⁇ [ ⁇ 1 , . . . , ⁇ 2000 ] of the matrix H and the 2000 sets of sample data into the formula (5), determining the output layer weight parameter ⁇ ; and substituting the ⁇ into the formula (6),
- the model function ⁇ ( ⁇ ) of the single hidden layer neural network of ⁇ is randomly generated, and the offset vector of the neuron is b i .
- the parameter variable ⁇ (k) is obtained by substituting the input parameter ⁇ (k) determined by the formula (26) into the model function ⁇ ( ⁇ ) of the determined single hidden layer neural network.
- the parameter variable ⁇ (k+1) can be obtained correspondingly.
- the parameter variables ⁇ (k+2);... ⁇ (k+19) can also be obtained in sequence.
- the Q and R matrices are unit matrices, and the above-mentioned parameters are substituted into inequality (14) to obtain a matrix P.
- the specific expression of the P matrix is shown in the following formula (28):
- the mass spring system is controlled by the above method, and the calculated control variable u( ⁇ ) is as shown by the solid line in FIG. 3, and the broken line is the linear quadratic regulator through the prior art ( The linear quadratic regulator (referred to as "LQR") determines the control variable u( ⁇ ).
- LQR linear quadratic regulator
- the controlled system is controlled, as shown in FIG. 4, the solid line is a variation curve x(k) of the state variable obtained by using the embodiment of the present invention, and the dotted line is the LQR. Determine the curve x(k) of the state variable versus time.
- the state variable obtained by the embodiment of the present invention tends to be faster than LQR, that is, the method of the embodiment of the present invention makes the spring system settle to the zero state more quickly, and the effect is obviously better than LQR.
- the size of the sequence numbers of the above processes does not mean the order of execution, and the order of execution of each process should be determined by its function and internal logic, and should not be taken to the embodiments of the present invention.
- the implementation process constitutes any limitation.
- the method for model predictive control is based on the state variable x(k) and the parameter variable ⁇ (k) at the current time k, and the control variable u(k-1) at the time k-1 at the previous time.
- the control increment ⁇ u(k) that satisfies the performance index of the prediction model is determined by a single-layer recurrent neural network algorithm, and the sum of the control increment ⁇ u(k) and the control variable u(k-1) at time k-1 is current
- the control variable u(k) at time k is finally subjected to model prediction control based on the control variable u(k).
- a data center ventilation and air conditioning system will be taken as an example to illustrate how to use the model predictive control method of the present invention to optimize the temperature and humidity of the data center.
- W z denote the indoor temperature
- T z denote the indoor temperature
- T sec denote the secondary coil temperature
- the control model can be obtained as shown in formula (1), where A( ⁇ (k)) and B( ⁇ (k)) are as shown in the following formula (29):
- V z is the zone volume
- W pri is the moisture content of the primary air
- W z is the zone moisture content
- ⁇ v is the time constant of the valve (time constant Of the valve)
- ⁇ is the gain consant.
- the matrix a matrix consisting of state variables x(k+1) to x(k+20) from time k+1 to k+10; matrix a matrix consisting of control variables u(k) to u(k+19) from time k to time k+9; matrix A matrix composed of control increments ⁇ u(k) to ⁇ u(k+19) from time k to time k+9, for any one of the control increments ⁇ u(k+j), can be expressed as shown in equation (10) .
- ⁇ (k) [ ⁇ 1 (k); ⁇ 2 (k); ⁇ 3 (k); ⁇ 4 (k); ⁇ 5 (k)].
- the input parameter ⁇ (k) is defined according to formula (3).
- the weight vector w i of the input layer to the hidden layer is randomly generated, and the offset vector of the neuron is b i .
- the excitation function g(s) of each neuron tanh(s), and substituting each of the above parameters into the formula (4), the neuron matrix H can be obtained.
- the output data ⁇ [ ⁇ 1 , . . . , ⁇ 2000 ] of the matrix H and the 2000 sets of sample data into the formula (5), determining the output layer weight parameter ⁇ ; and substituting the ⁇ into the formula (6),
- the model function ⁇ ( ⁇ ) of the single hidden layer neural network of ⁇ is randomly generated, and the offset vector of the neuron is b i .
- the input parameter ⁇ (k) determined according to the formula (31) is substituted into the model function ⁇ ( ⁇ ) of the determined single hidden layer neural network, and the parameter variable ⁇ ( ⁇ (k)) can be obtained, that is, according to ⁇ (k) Correspondence obtains ⁇ ( ⁇ (k)).
- the output signal ⁇ (k); ⁇ (k+1);...; ⁇ (k+9) can be calculated accordingly.
- the size of the sequence numbers of the above processes does not mean the order of execution, and the order of execution of each process should be determined by its function and internal logic, and should not be taken to the embodiments of the present invention.
- the implementation process constitutes any limitation.
- the method for model predictive control is based on the state variable x(k) and the parameter variable ⁇ (k) at the current time k, and the control variable u(k-1) at the time k-1 at the previous time. , through the single-layer recurrent neural network algorithm, determine the control increment ⁇ u(k) that satisfies the performance index of the prediction model, The sum of the control increment ⁇ u(k) and the control variable u(k-1) at time k-1 is the control variable u(k) at the current time k, and finally the model prediction is performed according to the control variable u(k). control.
- FIG. 5 shows a schematic block diagram of an apparatus 200 for model predictive control according to an embodiment of the present invention.
- each module in the apparatus 200 of the model predictive control may be integrated in one chip, for example, in a neuromorphic calculation.
- the various modules in the device 200 for predictive control of the model may be included on the chip.
- the apparatus 200 for predictive control of a model according to an embodiment of the present invention includes:
- a first determining module 210 configured to use a parameter variable ⁇ (k-1) to ⁇ (kq) at a time k1 from a k-1 time of the prediction model, a state variable x(k) at time k, and at the k- At least one of the control variables u(k-1) at time 1 determines a parameter variable ⁇ (k) at the time k;
- a second determining module 220 configured to, according to the state variable x(k), the control variable u(k-1), and the parameter variable ⁇ (k) determined by the first determining module, by a single layer recurrent neural network algorithm, Determining a control increment ⁇ u(k) that satisfies the performance model of the predictive model;
- the control module 240 is configured to perform model prediction control according to the control variable u(k) of the prediction model determined by the third determining module.
- the apparatus for predictive control of the embodiment of the present invention is based on the state variable x(k) and the parameter variable ⁇ (k) at the current time k, and the control variable u(k-1) at the time of the previous time k-1.
- the control increment ⁇ u(k) that satisfies the performance index of the prediction model is determined by a single-layer recurrent neural network algorithm, and the sum of the control increment ⁇ u(k) and the control variable u(k-1) at time k-1 is current
- the control variable u(k) at time k is finally subjected to model prediction control based on the control variable u(k).
- the first determining module 210 may be based on the prediction model at time k-1. Determining at least one of the parameter variables ⁇ (k-1) to ⁇ (kq) at time kq, the state variable x(k) at time k, and the control variable u(k-1) at the time k-1 The parameter variable ⁇ (k) at the time k.
- the model for the controlled object can be expressed as shown in the formula (1), wherein the state variable of the current time at the time k of the controlled object and the control variable at the time k-1 at the time k of the controlled object can be measured.
- the parameter variable ⁇ (k) can be based on the parameter variables ⁇ (k-1) to ⁇ (kq) of the prediction model at k-1 to kq, the state variable x(k) at time k, and At least one of the control variables u(k-1) at the k-1 time is determined by the first determining module 210.
- the parameter variable ⁇ (k) may be determined by using the prior art, or may be implemented by the present invention.
- the single hidden layer neural network determines the parameter variable ⁇ (k), and the present invention is not limited thereto.
- the first determining module 210 may model and estimate the parameter variable ⁇ (k) through a single hidden layer neural network.
- Neural network is a computational model that simulates the behavioral characteristics of human brain structure and performs distributed parallel information processing. Neural networks rely on their learning algorithms to adjust the interconnections between a large number of their internal neurons to achieve specific computational goals.
- the first determining module 210 can be a dedicated processor, and the processor can include a plurality of units, such as a matrix product unit, a matrix inversion unit, a random number generating unit, a nonlinear function mapping unit, a storage unit, and the like. Specifically, the operation of the processor may include two modes: offline training and online prediction.
- the offline training mode is mainly used to determine a configuration and a function relationship of each unit in the processor, for example, determining a model function ⁇ of a single hidden layer neural network (
- the online prediction mode is mainly used to determine the corresponding output data, for example, the parameter variable ⁇ (k) for determining the k time, based on the offline training result, but the present invention is not limited thereto.
- the model function ⁇ ( ⁇ ) of the single hidden layer neural network may be first determined by the first determining module 210.
- an input parameter ⁇ (k) may be defined by the formula (2), that is, The parameter variable ⁇ (k) at the current time can be expressed as a function F( ⁇ (k)) about the input parameter ⁇ (k). Since the input of the function is ⁇ (k), the output is the parameter variable ⁇ (k).
- the specific form of the model function ⁇ ( ⁇ ) of the single hidden layer neural network may be determined by the first determining module 210 in the offline training mode by the following method.
- s is the number of sample data, which is defined by the user.
- the larger the sample size the higher the accuracy, but the higher the sampling cost, so a reasonable sample size can be determined based on the empirical value.
- each ⁇ and ⁇ here correspond one-to-one, that is, for each input ⁇ i , an output ⁇ i can be correspondingly obtained.
- a single hidden layer neural network is constructed.
- the number of input layer neurons in the single hidden layer neural network is n+m+pq, n is the dimension of the state variable x(k), m is the dimension of the control variable u(k); the number of neurons in the output layer is p,p
- the dimension of ⁇ (k); the number of hidden layer neurons is L, the value of L can be defined by the user; the excitation function of the hidden layer neurons is g( ⁇ ), and g( ⁇ ) can be determined by empirical values;
- the weight vector of the input layer to the hidden layer is w i
- the bias vector of the neuron is b i
- w i and b i can be randomly generated.
- Substituting the obtained matrix ⁇ and the output ⁇ [ ⁇ 1 , . . . , ⁇ s in the s samples into the formula (5), obtaining the weight parameter ⁇ of the single hidden layer neural network neuron connected to the output layer,
- the model function ⁇ ( ⁇ ) of the single hidden layer neural network that determines completion of training is expressed as equation (6), where ⁇ i is the ith row of the matrix of the weight parameter ⁇ .
- the input parameter ⁇ (k) defined by the formula (3) is input, and is substituted into the formula (6) to obtain the parameter variable ⁇ (k) at time k.
- the first determining module 210 determines the parameter variable ⁇ (k) at time k, it may be substituted into the formula (1), and the state variable x(k+1) at the time k+1 may be determined.
- the parameter variable ⁇ (k+1) at time k+1 can be determined, and so on, for determining the parameter variable ⁇ at the time of k+N at an arbitrary time. (k+N), firstly, according to the parameter variable ⁇ (k) at time k and the predicted control variable u'(k+N-1) at time k+N-1, the k+N time can be obtained by the formula (7).
- Equation (7) is the deformation form of equation (1) at time k+N
- A( ⁇ ( ⁇ )) is the first reference function for ⁇ ( ⁇ )
- B( ⁇ ( ⁇ )) is a second reference function for ⁇ ( ⁇ )
- N is a positive integer.
- the input parameter ⁇ (k+N) can be similarly determined by equation (3).
- the parameter variable ⁇ (k+N) at the time k+N can be obtained.
- the unknown parameter is modeled and estimated by using a single hidden layer neural network, and the model mismatch problem in the predictive control of the linear variable parameter system is better solved.
- the neural network has a simple structure and a fast training speed, avoids complicated iterative training of the traditional neural network, and improves the calculation efficiency.
- the second determining module 220 passes the single layer recurrent neural network algorithm, according to the state variable x(k), the control variable u(k-1), and the first determining module 210, the parameter variable ⁇ (k And determining a control increment ⁇ u(k) that satisfies the performance model of the prediction model.
- the second determining module 220 may also be a recurrent neural network module, and may be composed of a dedicated processor, where the processor may include a matrix product unit, a matrix summation unit, a max function unit, and a random number generating unit. Wait for multiple units.
- the second determining module 220 may define several parameters from the time k to the time k+N, as shown in the formula (9), wherein the matrix x(k) a matrix consisting of state variables x(k+1) to x(k+N) from time k+1 to k+N; matrix u(k) is the control variable u from time k to k+N-1 ( k) a matrix composed of u(k+N-1); the matrix ⁇ u(k) is a matrix composed of control increments ⁇ u(k) to ⁇ u(k+N-1) from time k to k+N-1 For any one of the control increments ⁇ u(k+j), it can be expressed as shown in equation (10).
- the formula (1) can be expressed as shown in the formula (11), wherein the matrices S, V, and M are respectively expressed as shown in the formula (12), wherein A ( ⁇ ( ⁇ )) is the first reference function for ⁇ ( ⁇ ), B( ⁇ ( ⁇ )) is the second reference function for ⁇ ( ⁇ ), which is related to the controlled object; ⁇ ( ⁇ ) can be the first
- the parameter variables at various times determined by the module 210 are determined.
- the performance index of the MPC is expressed as shown in the formula (13), wherein Q and R are arbitrary positive definite diagonal matrices, which can be defined by the user, and P satisfies inequality (14).
- K is an auxiliary variable.
- the second determining module 220 can solve the constraint optimization problem online by designing a single-layer recurrent neural network, and the neural network model and the self-learning method can be defined by the formula (20), that is, according to the formula (20) Determine the control increment for the time from k to k+N-1 in equation (9) Where ⁇ is a sufficiently large positive real number whose specific value can be defined by the user.
- the neural network can converge from any initial state to the global optimal solution corresponding to the constrained optimization problem.
- the control increment of time k to k+N-1 can be determined by the above formula (20).
- the recursive neural network is used to calculate the optimal control variable online, that is, the optimal control signal, and the calculation efficiency is high and the real-time performance is good.
- the number of neurons in the neural network and the learning algorithm are quantitatively and qualitatively given, and the implementation is simple and convenient, and no internal adjustment of internal parameters is required.
- the summation can obtain the control variable u(k) at the current time, and so on, and the third determining module 230 can calculate the control increment for the time k+N-1.
- the control increment By summing the control increment with the control variable u(k+N-2) of the previous time k+N-2, the control variable u(k+N-1) at time k+N-1 can be obtained.
- the invention is not limited to this.
- control variable u(k+N-1) at the time k+N-1 and the state variable x(k+N-1) obtained in the real-time measurement are substituted into the formula (7),
- the state variable x(k+N) at the time k+N, and so on, obtains the state variable and the control variable at any time after the k time and the k time, and the present invention is not limited thereto.
- control module 240 performs model prediction control according to the control variable u(k) of the prediction model determined by the third determining module 230.
- the apparatus 200 for predictive control of a model may correspond to the method 100 of performing model predictive control in an embodiment of the present invention, and the above and other operations of the various modules in the apparatus 200 of the model predictive control and/or Or function to achieve each of the figures in Figure 1 to Figure 2 The corresponding process of the method is not repeated here for the sake of brevity.
- the apparatus for predictive control of the embodiment of the present invention is based on the state variable x(k) and the parameter variable ⁇ (k) at the current time k, and the control variable u(k-1) at the time of the previous time k-1.
- the control increment ⁇ u(k) that satisfies the performance index of the prediction model is determined by a single-layer recurrent neural network algorithm, and the sum of the control increment ⁇ u(k) and the control variable u(k-1) at time k-1 is current
- the control variable u(k) at time k is finally subjected to model prediction control based on the control variable u(k).
- the embodiment of the present invention further provides a device 300 for predictive control of a model, including a processor 310, a memory 320, and a bus system 330.
- the processor 310 and the memory 320 are connected by a bus system 330 for storing instructions for executing instructions stored by the memory 320.
- the memory 320 stores the program code, and the processor 310 can call the program code stored in the memory 320 to perform the following operations: the parameter variables ⁇ (k-1) to ⁇ (kq) according to the prediction model at time k-1 to kq.
- the apparatus for predictive control of the embodiment of the present invention is based on the state variable x(k) and the parameter variable ⁇ (k) at the current time k, and the control variable u(k-1) at the time of the previous time k-1.
- the control increment ⁇ u(k) that satisfies the performance index of the prediction model is determined by a single-layer recurrent neural network algorithm, and the sum of the control increment ⁇ u(k) and the control variable u(k-1) at time k-1 is current
- the control variable u(k) at time k is finally subjected to model prediction control based on the control variable u(k).
- the processor 310 may be a central processing unit (“CPU"), and the processor 310 may also be other general-purpose processors.
- DSP digital signal processor
- ASIC application specific integrated circuit
- FPGA off-the-shelf programmable gate array
- the general purpose processor may be a microprocessor or the processor or any conventional processor or the like.
- the memory 320 can include read only memory and random access memory and provides instructions and data to the processor 310. A portion of the memory 320 may also include a non-volatile random access memory. For example, the memory 320 can also store information of the device type.
- the bus system 330 may include a power bus, a control bus, a status signal bus, and the like in addition to the data bus. However, for clarity of description, various buses are labeled as bus system 330 in the figure.
- each step of the foregoing method may be completed by an integrated logic circuit of hardware in the processor 310 or an instruction in a form of software.
- the steps of the method disclosed in the embodiments of the present invention may be directly implemented as a hardware processor, or may be performed by a combination of hardware and software modules in the processor.
- the software module can be located in a conventional storage medium such as random access memory, flash memory, read only memory, programmable read only memory or electrically erasable programmable memory, registers, and the like.
- the storage medium is located in the memory 320, and the processor 310 reads the information in the memory 320 and combines the hardware to perform the steps of the above method. To avoid repetition, it will not be described in detail here.
- the processor 310 may call the program code stored in the memory 320 to perform the following operations: the parameter variable ⁇ (k) according to the k time, the state variable x(k), and k+N-
- the processor 310 may call the program code stored in the memory 320 to perform the following operations: determining, by the single layer recursive neural network algorithm, the control increment ⁇ u(k) according to the following formula:
- A( ⁇ ( ⁇ )) is the first reference function for ⁇ ( ⁇ )
- B( ⁇ ( ⁇ )) is the second reference function for ⁇ ( ⁇ )
- the matrix consisting of the last n rows of S, V, and M, where n is the dimension of the state variable x(k), and [-u min +u(k-1)] is -u min +u for each row.
- K is an auxiliary variable.
- the processor 310 may invoke the program code stored in the memory 320 to perform the following operations: determining, by the single layer recursive neural network algorithm, the time from k to k+N-1 according to formula (20) Control increment
- the matrices S, V, and M satisfy the formula (12), respectively
- a ( ⁇ ( ⁇ )) is the first reference function for ⁇ ( ⁇ )
- B ( ⁇ ( ⁇ )) is the second reference function for ⁇ ( ⁇ )
- n is the dimension of the state variable x(k)
- the processor 310 may invoke the program code stored in the memory 320 to perform the following operations: the control increment according to the k time to the k+N-1 time. And the control variable from the time k-1 to the time k+N-2 Determining the control variable from the time k to the time k+N-1 among them, According to the control variable from the k time to the k+N-1 time Perform model prediction control.
- the apparatus 300 for model predictive control may correspond to the apparatus 200 for model predictive control in the embodiment of the present invention, and may correspond to executing a corresponding subject in the method 100 according to an embodiment of the present invention, and
- the foregoing and other operations and/or functions of the respective modules in the model predictive control device 300 are respectively omitted in order to implement the corresponding processes of the respective methods in FIG. 1 to FIG. 2 for brevity.
- the apparatus for predictive control of the embodiment of the present invention is based on the state variable x(k) and the parameter variable ⁇ (k) at the current time k, and the control variable u(k-1) at the time of the previous time k-1. Pass Through a single-layer recurrent neural network algorithm, the control increment ⁇ u(k) that satisfies the performance index of the prediction model is determined, and the sum of the control increment ⁇ u(k) and the control variable u(k-1) at time k-1 is the current time. The control variable u(k) at time k, and finally model prediction control based on the control variable u(k).
- the disclosed systems, devices, and methods may be implemented in other manners.
- the device embodiments described above are merely illustrative.
- the division of the unit is only a logical function division.
- there may be another division manner for example, multiple units or components may be combined or Can be integrated into another system, or some features can be ignored or not executed.
- the mutual coupling or direct coupling or communication connection shown or discussed may be an indirect coupling or communication connection through some interface, device or unit, and may be in an electrical, mechanical or other form.
- the units described as separate components may or may not be physically separated, and the components displayed as units may or may not be physical units, that is, may be located in one place, or may be distributed to multiple network units. Some or all of the units may be selected according to actual needs to achieve the purpose of the solution of the embodiment.
- each functional unit in each embodiment of the present invention may be integrated into one processing unit, or each unit may exist physically separately, or two or more units may be integrated into one unit.
- the functions may be stored in a computer readable storage medium if implemented in the form of a software functional unit and sold or used as a standalone product. Based on such understanding, the technical solution of the present invention is essentially or a part contributing to the prior art or a part of the technical solution.
- the points may be embodied in the form of a software product stored in a storage medium, including instructions for causing a computer device (which may be a personal computer, server, or network device, etc.) to perform various embodiments of the present invention All or part of the steps of the method.
- the foregoing storage medium includes: a U disk, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disk, and the like. .
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Abstract
一种模型预测控制的方法和装置,该方法包括:确定在k时刻的参数变量θ(k)(S110);通过单层递归神经网络算法,根据k-1时刻的控制变量u(k-1)、k时刻的状态变量x(k)和参数变量θ(k),确定满足预测模型性能指标的控制增量Δu(k)(S120);将该预测模型的该控制变量u(k-1)和该控制增量Δu(k)之和确定为该预测模型在该k时刻的控制变量u(k)(S130);根据该预测模型的该控制变量u(k),进行模型预测控制(S140)。根据当前时刻k时刻的状态变量x(k)和参数变量θ(k),以及前一时刻的控制变量u(k-1),通过单层递归神经网络算法,确定满足预测模型性能指标的控制变量u(k),根据该控制变量u(k),进行模型预测控制,能够提高计算效率,可以保证性能指标的可靠性。
Description
本发明涉及信息技术领域,尤其涉及模型预测控制的方法和装置。
模型预测控制(Model Predictive Control,简称“MPC”)是一种采取有限时域多步预测、滚动优化和反馈矫正的控制策略,广泛应用于网络化控制、资源调度管理等多个领域。MPC的核心思想是在每一个采样时刻对被控***未来N个有限时刻的状态进行预测,进而通过求解一个有限时域最优控制问题以获得当前时刻的最优控制信号。
对于一个一般性的离散***模型x(k+1)=f(x(k),u(k)),其中x是n维状态变量,u是m维控制信号,f表示***模型,k是当前采样时刻,k+1表示下一采样时刻。该***的MPC问题可以描述为:
s.t.x(k+j+1)=f(x(k+j),u(k+j)),j=1,...,N-1
umin≤u(k+j)≤umax,j=0,...,N-1
xmin≤x(k+j)≤xmax,j=1,...,N
其中,J(k)是控制***的性能指标,Q和R为系数矩阵,可以根据实际应用设置为相应的矩阵;F(x(k+N))为关于状态变量x(k+N)的函数,该函数可以根据实际应用进行设置;umax和umin分别是控制输入的约束上界和下界,xmax和xmin分别是***状态的约束上界和下界,N为预测步长。
具体地,考虑一个线性变参数***x(k+1)=A(θ(k))x(k)+B(θ(k))u(k),其中θ是p维的不确定参数。一般地,当前时刻的参数变量θ(k)可测量获得,将来任意时刻的θ取值范围已知但是其具体的函数表达式未知。针对这一类带有不确定参数***的MPC问题,一个广泛采用的技术方案是min-max优化方法,即对所有θ的可能影响所造成的最差情况做优化设计。通过优化目标函数的上界,采用线性矩阵不等式这一工具将线性变参数***的MPC问题转化为线性矩阵不等式优化问题:
minγ,Q,Y,X,Lγ
这里*代表对称矩阵相应的项,s代表θ可能产生的情形数。在每个采样时刻对上述矩阵不等式优化问题求解后,控制***的最优控制信号为u(k)=YQ-1x(k)。
该技术的最大问题在于其计算的保守性。在MPC框架下设计最优控制信号,其目标是使得***特定的性能指标取得最好的表现。现有的最小最大(min-max)优化方案考虑了***所可能出现的最差情况,但是对于被控对象来讲,其每一个时刻的表现形式是确定的,而且往往不会呈现最差的情形。在这种情况下,对性能指标的最差情况做优化,无疑牺牲了整体控制性能。另外,MPC最优控制信号的获得是基于对***未来预测状态的优化,如果被控***的模型f(x,u)与实际被控对象之间存在较大误差,那么所得到的最优控制信号就难以获得令人满意的控制效果。
发明内容
本发明提供了一种模型预测控制的方法和的装置,能够提高计算效率,保证模型预测控制的性能指标的可靠性。
第一方面,提供了一种模型预测控制的方法,该方法包括:根据预测模型在k-1时刻的至k-q时刻的参数变量θ(k-1)至θ(k-q)、在k时刻的状态变量x(k)以及在该k-1时刻的控制变量u(k-1)中的至少一个,确定在该k时刻的参数变量θ(k);通过单层递归神经网络算法在线求解二次规划问题,根据该状态变量x(k)、该控制变量u(k-1)和该参数变量θ(k),确定满足该预测模型性能指标的控制增量Δu(k);根据该预测模型的该控制变量u(k-1)和该控
制增量Δu(k),确定该预测模型在该k时刻的控制变量u(k),其中,u(k)=u(k-1)+Δu(k);根据该预测模型的该控制变量u(k),进行模型预测控制。
结合第一方面,在第一方面的一种实现方式中,该根据预测模型在k-1时刻的至k-q时刻的参数变量θ(k-1)至θ(k-q)、在k时刻的状态变量x(k)以及在该k-1时刻的控制变量u(k-1)中的至少一个,确定在该k时刻的参数变量θ(k),包括:确定单隐藏层神经网络的模型函数θ(α);根据该预测模型的该状态变量x(k)、在该k时刻的预测控制变量u'(k)以及该k-1时刻至该k-q时刻的该参数变量θ(k-1)至θ(k-q),确定输入参数α(k)=[x(k);u'(k);θ(k-1);...;θ(k-q)],其中,q为整数,1≤q<k;将该输入参数α(k)代入该模型函数θ(α)中,计算得到该k时刻的该参数变量θ(k)。
结合第一方面及其上述实现方式,在第一方面的另一种实现方式中,该确定单隐藏层神经网络的模型函数θ(α),包括:确定s组输入数据α=[α1,…,αs]和对应的s组输出数据θ=[θ1,…,θs];构建该单隐藏层神经网络,该单隐藏层神经网络的输入层神经元数目为n+m+pq,隐藏层神经元的数目为L,输出层神经元数目为p,隐藏层神经元激励函数为g(·),第i个输入层到隐藏层的权值向量为wi,神经元的偏置向量为bi,其中,n为该状态变量x(k)的维度,m为该控制变量u(k)的维度;根据该单隐藏层神经网络、该输入数据α=[α1,…,αs]和该输出数据θ=[θ1,…,θs],确定该单隐藏层神经网络神经元与输出层相连的权重参数β=HT(I+HHT)-1[θ1,...,θs],其中:
确定该模型函数θ(α):
其中,βi为该权重参数β的第i行。
结合第一方面及其上述实现方式,在第一方面的另一种实现方式中,该方法还包括:根据该k时刻的该参数变量θ(k)、该状态变量x(k)以及k+N-1时刻的预测控制变量u'(k+N-1),通过下面的公式,确定该预测模型在k+N时刻的该状态变量x(k+N):
x(k+N)=A(θ(k+N-1))x(k+N-1))+B(θ(k+N-1))u'(k+N-1))
其中A(θ(·))为关于θ(·)的第一参考函数,B(θ(·))为关于θ(·)的第二参考函数,N为时间步长,N为正整数;根据该状态变量x(k+N)、在该k+N时刻的预测控制变量u'(k+N)以及k+N-1时刻至k+N-q时刻的参数变量θ(k+N-1)至θ(k+N-q),确定输入参数α(k+N)=[x(k+N);u'(k+N);θ(k+N-1);...;θ(k+N-q)],其中,q为整数,1≤q<k;将该输入参数α(k+N)代入该模型函数θ(α)中,计算得到该k+N时刻的该参数变量θ(k+N)。
结合第一方面及其上述实现方式,在第一方面的另一种实现方式中,该通过单层递归神经网络算法在线求解二次规划问题,根据该状态变量x(k)、该控制变量u(k-1)和该参数变量θ(k),确定满足该预测模型性能指标的控制增量Δu(k),包括:通过该单层递归神经网络算法,根据下面的公式确定该控制增量Δu(k):
A(θ(·))为关于θ(·)的第一参考函数,B(θ(·))为关于θ(·)的第二参考函数,和分别为S、V和M的后n行构成的矩阵,n为该状态变量x(k)的维度,-umin+u(k-1)为每一行均为-umin+u(k-1)的m行矩阵,umax-u(k-1)为每一行均为umax-u(k-1)的m行矩阵,m为该控制变量u(k)的维度,λ为
正实数,umax和umin表示该预测模型的控制变量最大值和最小值,xmax和xmin表示该预测模型的状态变量最大值和最小值,Q和R为任意正定对角矩阵,P满足下面的不等式:
Q+KTRK+(A(θ(k+1))+B(θ(k+1))K)TP(A(θ(k+1))+B(θ(k+1))K)-P≤0
其中,P>0,K为辅助变量。
结合第一方面及其上述实现方式,在第一方面的另一种实现方式中,该方法还包括:通过该单层递归神经网络算法在线求解二次规划问题,根据下面的公式确定该k时刻至k+N-1时刻的控制增量
Δu(k+j)=u(k+j)-u(k+j-1)],0≤j≤N,A(θ(·))为关于θ(·)的第一参考函数,B(θ(·))为关于θ(·)的第二参考函数,和分别为S、V和M的后n行构成的矩阵,n为该状态变量x(k)的维度,为每一行均为的m*N行矩阵,为每一行均为的m*N行矩阵,m为该控制变量u(k)的维度,N为时间步长,λ为正实数,和表示该预测模型的控制变量最大值和最小值,和表示该预测模型的状态变量最大值和最小值,Q和R为任意正定对角矩阵,P满足下面的不等式:
Q+KTRK+(A(θ(k+N))+B(θ(k+N))K)TP(A(θ(k+N))+B(θ(k+N))K)-P≤0
其中,P>0,K为辅助变量。
结合第一方面及其上述实现方式,在第一方面的另一种实现方式中,该方法还包括:根据该k时刻至该k+N-1时刻的该控制增量以及该k-1时刻至k+N-2时刻的控制变量确定该k时刻至该k+N-1时刻的控制变量 其中, 根据该k时刻至该k+N-1时刻的控制变量进行模型预测控制。
第二方面,提供了一种模型预测控制的的装置,该装置包括:第一确定模块,用于根据预测模型在k-1时刻的至k-q时刻的参数变量θ(k-1)至θ(k-q)、在k时刻的状态变量x(k)以及在该k-1时刻的控制变量u(k-1)中的至少一个,确定在该k时刻的参数变量θ(k);第二确定模块,用于通过单层递归神经网络算法在线求解二次规划问题,根据该状态变量x(k)、该控制变量u(k-1)和该第一确定模块确定的该参数变量θ(k),确定满足该预测模型性能指标的控制增量Δu(k);第三确定模块,用于根据该预测模型的该控制变量u(k-1)和该第二确定模块确定的该控制增量Δu(k),确定该预测模型在该k时刻的控制变量u(k),其中,u(k)=u(k-1)+Δu(k);控制模块,用于根据该第三确定模块确定的该预测模型的该控制变量u(k),进行模型预测控制。
结合第二方面及其上述实现方式,在第二方面的另一种实现方式中,该第一确定模块具体用于:确定s组输入数据α=[α1,…,αs]和对应的s组输出数据θ=[θ1,…,θs];构建该单隐藏层神经网络,该单隐藏层神经网络的输入层神经元数目为n+m+pq,隐藏层神经元的数目为L,输出层神经元数目为p,隐藏层神经元激励函数为g(·),第i个输入层到隐藏层的权值向量为wi,神
经元的偏置向量为bi,其中,n为该状态变量x(k)的维度,m为该控制变量u(k)的维度;根据该单隐藏层神经网络、该输入数据α=[α1,…,αs]和该输出数据θ=[θ1,…,θs],确定该单隐藏层神经网络神经元与输出层相连的权重参数β=HT(I+HHT)-1[θ1,...,θs],其中:
确定该模型函数θ(α):
其中,βi为该权重参数β的第i行。
结合第二方面,在第二方面的一种实现方式中,该第一确定模块具体用于:确定单隐藏层神经网络的模型函数θ(α);根据该预测模型的该状态变量x(k)、在该k时刻的预测控制变量u'(k)以及该k-1时刻至该k-q时刻的该参数变量θ(k-1)至θ(k-q),确定输入参数α(k)=[x(k);u'(k);θ(k-1);...;θ(k-q)],其中,q为整数,1≤q<k;将该输入参数α(k)代入该模型函数θ(α)中,计算得到该k时刻的该参数变量θ(k)。
结合第二方面及其上述实现方式,在第二方面的另一种实现方式中,该第一确定模块具体用于:根据该k时刻的该参数变量θ(k)、该状态变量x(k)以及k+N-1时刻的预测控制变量u'(k+N-1),通过下面的公式,确定该预测模型在k+N时刻的该状态变量x(k+N):
x(k+N)=A(θ(k+N-1))x(k+N-1))+B(θ(k+N-1))u'(k+N-1))
其中A(θ(·))为关于θ(·)的第一参考函数,B(θ(·))为关于θ(·)的第二参考函数,N为时间步长,N为正整数;根据该状态变量x(k+N)、在该k+N时刻的预测控制变量u'(k+N)以及k+N-1时刻至k+N-q时刻的参数变量θ(k+N-1)至θ(k+N-q),确定输入参数α(k+N)=[x(k+N);u'(k+N);θ(k+N-1);...;θ(k+N-q)],其中,q为整数,1≤q<k;将该输入参数α(k+N)代入该模型函数θ(α)中,计算得到该k+N时刻的该参数变量θ(k+N)。
结合第二方面及其上述实现方式,在第二方面的另一种实现方式中,该第二确定模块具体用于:通过该单层递归神经网络算法,根据下面的公式确
定该控制增量Δu(k):
A(θ(·))为关于θ(·)的第一参考函数,B(θ(·))为关于θ(·)的第二参考函数,和分别为S、V和M的后n行构成的矩阵,n为该状态变量x(k)的维度,-umin+u(k-1)为每一行均为-umin+u(k-1)的m行矩阵,umax-u(k-1)为每一行均为umax-u(k-1)的m行矩阵,m为该控制变量u(k)的维度,λ为正实数,umax和umin表示该预测模型的控制变量最大值和最小值,xmax和xmin表示该预测模型的状态变量最大值和最小值,Q和R为任意正定对角矩阵,P满足下面的不等式:
Q+KTRK+(A(θ(k+1))+B(θ(k+1))K)TP(A(θ(k+1))+B(θ(k+1))K)-P≤0
其中,P>0,K为辅助变量。
Δu(k+j)=u(k+j)-u(k+j-1)],0≤j≤N,A(θ(·))为关于θ(·)的第一参考函数,B(θ(·))为关于θ(·)的第二参考函数,和分别为S、V和M的后n行构成的矩阵,n为该状态变量x(k)的维度,为每一行均为的m*N行矩阵,为每一行均为的m*N行矩阵,m为该控制变量u(k)的维度,N为时间步长,λ为正实数,和表示该预测模型的控制变量最大值和最小值,和表示该预测模型的状态变量最大值和最小值,Q和R为任意正定对角矩阵,P满足下面的不等式:
Q+KTRK+(A(θ(k+N))+B(θ(k+N))K)TP(A(θ(k+N))+B(θ(k+N))K)-P≤0
其中,P>0,K为辅助变量。
结合第二方面及其上述实现方式,在第二方面的另一种实现方式中,该第三确定模块还用于:根据该k时刻至该k+N-1时刻的该控制增量以及该k-1时刻至k+N-2时刻的控制变量
确定该k时刻至该k+N-1时刻的控制变量 其中, 根据该k时刻至该k+N-1时刻的控制变量进行模型预测控制。
基于上述技术方案,本发明实施例的模型预测控制的方法和装置,根据当前时刻k时刻的状态变量x(k)和参数变量θ(k),以及前一时刻k-1时刻的控制变量u(k-1),通过单层递归神经网络算法,确定满足预测模型性能指标的控制增量Δu(k),该控制增量Δu(k)与k-1时刻的控制变量u(k-1)的和为当前时刻k时刻的控制变量u(k),最后根据该控制变量u(k),进行模型预测控制。因此能够获得较现有技术更为优化的当前时刻控制变量,从而能够提高计算效率,从理论上保证了性能指标的准确度,即使得闭环控制***是渐进稳定的,并且整个模型预测控制***高度自主运行,实现了自动化操作。
为了更清楚地说明本发明实施例的技术方案,下面将对本发明实施例中所需要使用的附图作简单地介绍,显而易见地,下面所描述的附图仅仅是本发明的一些实施例,对于本领域普通技术人员来讲,在不付出创造性劳动的前提下,还可以根据这些附图获得其他的附图。
图1是根据本发明实施例的模型预测控制的方法的示意性流程图。
图2是根据本发明实施例的单隐藏层神经网络结构的示意图。
图3是根据本发明实施例的质量弹簧***的控制变量对比的示意图。
图4是根据本发明实施例的质量弹簧***的状态变量对比的示意图。
图5是根据本发明实施例的模型预测控制的装置的示意性框图。
图6是根据本发明实施例的模型预测控制的装置的另一示意性框图。
下面将结合本发明实施例中的附图,对本发明实施例中的技术方案进行清楚、完整地描述,显然,所描述的实施例是本发明的一部分实施例,而不是全部实施例。基于本发明中的实施例,本领域普通技术人员在没有做出创造性劳动的前提下所获得的所有其他实施例,都应属于本发明保护的范围。
图1示出了根据本发明实施例的模型预测控制的方法100的示意性流程图。如图1所示,该方法100包括:
S110,根据预测模型在k-1时刻的至k-q时刻的参数变量θ(k-1)至θ(k-q)、在k时刻的状态变量x(k)以及在该k-1时刻的控制变量u(k-1)中的至少一个,确定在该k时刻的参数变量θ(k);
S120,通过单层递归神经网络算法在线求解二次规划问题,根据该状态变量x(k)、该控制变量u(k-1)和该参数变量θ(k),确定满足该预测模型性能指标的控制增量Δu(k);
S130,根据该预测模型的该控制变量u(k-1)和该控制增量Δu(k),确定该预测模型在该k时刻的控制变量u(k),其中,u(k)=u(k-1)+Δu(k);
S140,根据该预测模型的该控制变量u(k),进行模型预测控制。
具体地,获取预测模型在k时刻的状态变量x(k)以及在k-1时刻的控制变量u(k-1),根据该状态变量x(k)以及控制变量u(k-1),确定在该k时刻的参数变量θ(k),可选地,可以通过训练单隐藏层神经网络的模型确定该参数变量θ(k);通过单层递归神经网络算法,根据状态变量x(k)、控制变量u(k-1)和参数变量θ(k),确定满足该预测模型性能指标的控制增量Δu(k),该控制增量Δu(k)与k-1时刻的控制变量u(k-1)的和为当前时刻k时刻的控制变量u(k),通过该当前时刻k时刻的控制变量,进行模型预测控制。
可选地,本发明实施例的方法可以通过神经网络架构完成,例如,该方法中的确定参数变量θ(k)的预测过程与确定控制增量Δu(k)的在线优化过程等都可以通过神经网络架构完成,并且该神经网络架构可以通过一个神经形态计算芯片完成,本发明并不限于此。
因此,本发明实施例的模型预测控制的方法,根据当前时刻k时刻的状态变量x(k)和参数变量θ(k),以及前一时刻k-1时刻的控制变量u(k-1),通过单层递归神经网络算法,确定满足预测模型性能指标的控制增量Δu(k),该控制增量Δu(k)与k-1时刻的控制变量u(k-1)的和为当前时刻k时刻的控制变量u(k),最后根据该控制变量u(k),进行模型预测控制。因此能够获得较现有技术更为优化的当前时刻控制变量,从而能够提高计算效率,从理论上保证了性能指标的准确度,即使得闭环控制***是渐进稳定的,并且整个模型预测控制***高度自主运行,实现了自动化操作。
在本发明实施例中,对于一个有优化需求的控制问题,具体表现在被控对象的模型可以表示为如公式(1)的形式:
x(k+1)=A(θ(k))x(k)+B(θ(k))u(k) (1)
其中x(k)是***在当前时刻k时刻的状态变量,可以从受控过程中实时测量获得;u(k)是***在当前时刻k时刻的控制变量,即控制信号,是当前未知的;A(θ(·))和B(θ(·))是受控过程中与参数变量θ(k)有关的参考函数,可以看做参数矩阵的形式,其具体形式依赖于参数变量θ(k)的取值,θ(k)是可以从受控过程中实时测量得到的。该控制问题有一个已知的目标输出,控制目标为通过设计u(k)使得受控过程的实际输出与目标输出趋近于相等。
可选地,本发明实施例的典型用例包括:数据中心的资源管理,机器人的自动控制,半导体生产的供应链管理,楼宇节能控制,无人机飞行控制等。这些用例的一个显著共性特征为他们的控制目标都是为了实现描述全局***行为的某一个性能指标的最优化,而物理条件的约束限定了所能采取的控制行为的范围。在可行的范围里,总是存在一个控制行为使得描述全局***的性能指标取得最小值。例如,对于数据中心的资源管理,一个重要的全局性能指标就是***整体能耗,在这种情况下,预测控制的状态变量可以包括数据中心的温度、功耗或资源利用率等,控制信号可以是风扇/空调的转速、CPU线程分配指令等,但本发明并不限于此。
在S110中,根据预测模型在k-1时刻的至k-q时刻的参数变量θ(k-1)至θ(k-q)、在k时刻的状态变量x(k)以及在该k-1时刻的控制变量u(k-1)中的至少一个,确定在该k时刻的参数变量θ(k)。具体地,对于被控对象的模型可以表示为如公式(1)所示,其中,被控对象当前时刻k时刻的状态变量以及k时刻的前一时刻k-1时刻的控制变量,可以通过测量实时获取得到;而参数变量θ(k)可以根据预测模型在k-1时刻的至k-q时刻的参数变量θ(k-1)至θ(k-q)、在k时刻的状态变量x(k)以及在该k-1时刻的控制变量u(k-1)中的至少一个确定,具体地,可以利用现有技术确定该参数变量θ(k),也可以通过本发明实施例中单隐藏层神经网络确定该参数变量θ(k),本发明并不限于此。
可选地,可以通过单隐藏层神经网络对该参数变量θ(k)进行建模和在线估计。神经网络是一种模拟人脑结构行为特征进行分布式并行信息处理的计算模型。神经网络依靠其学习算法调整其内部大量神经元之间的相互连接关系,从而达到特定的计算目的。首先可以确定单隐藏层神经网络的模型函数θ(α),具体地,可以通过下面的公式(2)定义一个输入参数α(k):
θ(k)=F(x(k),u(k),θ(k-1),...,θ(k-q))=F(α(k)) (2)
即对于当前时刻的参数变量θ(k),可以表示为一个关于输入参数α(k)的函数F(α(k)),由于该函数的输入为α(k),输出为参数变量θ(k),即可以表示为一个模型函数θ(α),其中输入参数α(k)满足下面的公式(3):
α(k)=[x(k);u'(k);θ(k-1);...;θ(k-q)] (3)
其中,x(k)为当前时刻k时刻的状态变量;u'(k)为当前时刻的控制变量的预测量,即预测控制变量;k-1时刻至k-q时刻的参数变量为θ(k-1)至θ(k-q),其中q为时间常数,可以由用户进行定义。
具体地,可以通过下面的方法确定该单隐藏层神经网络的模型函数θ(α)的具体形式。首先对被控对象进行离线分析,可以获得两组数据θ=[θ1,…,θs]以及α=[α1,…,αs],其中s是样本数据的数量,由用户进行定义,样本数量越大,准确度越高,但是采样成本越高,因此可以根据经验值确定合理的样本数量。另外,这里的每个α和θ一一对应,即对于每个输入αi,对应地可以获得一个输出θi。
如图2所示,构建单隐藏层神经网络。该单隐藏层神经网络的输入层神经元数目为n+m+pq,n为状态变量x(k)的维度,m为控制变量u(k)的维度;输出层神经元数目为p,p为θ(k)的维度;隐藏层神经元的数目为L,L的值可以由用户进行定义;隐藏层神经元激励函数为g(·),g(·)可以由经验值确定;第i个输入层到隐藏层的权值向量为wi,神经元的偏置向量为bi,wi和bi可以随机产生。
将样本中的输入参数α=[α1,…,αs]代入下面的公式(4)中,获得神经元矩阵H:
将获得的矩阵H以及s个样本中的输出θ=[θ1,…,θs]代入下面的公式(5)中,获得该单隐藏层神经网络神经元与输出层相连的权重参数β:
β=HT(I+HHT)-1[θ1,...,θs] (5)
则可以确定完成训练的该单隐藏层神经网络的模型函数θ(α)表示为公式(6):
其中,βi为权重参数β的矩阵的第i行。
因此,对于当前时刻k时刻,以公式(3)定义的输入参数α(k)为输入,代入公式(6)中,即可获得k时刻的参数变量θ(k)。
在本发明实施例中,当确定了k时刻的参数变量θ(k)后,可以代入公式(1)中,可以确定k+1时刻的状态变量x(k+1),再根据k+1时刻的预测的控制变量u'(k+1),可以确定k+1时刻的参数变量θ(k+1),依次类推,对于确定任意时刻k+N时刻的参数变量θ(k+N),N为预测步长。首先根据k时刻的参数变量θ(k)以及k+N-1时刻的预测控制变量u'(k+N-1),通过下面的公式(7),可以获得k+N时刻的状态变量x(k+N):
x(k+N)=A(θ(k+N-1))x(k+N-1)+B(θ(k+N-1))u'(k+N-1) (7)
其中,该公式(7)为公式(1)在时刻k+N时刻的变形形式,A(θ(·))为关于θ(·)的第一参考函数,B(θ(·))为关于θ(·)的第二参考函数,N为正整数。
对于确定的k+N时刻的状态变量x(k+N)以及k+N时刻的预测控制变量u(k+N),可以类似的通过公式(3)确定输入参数α(k+N)如公式(8)所示:
α(k+N)=[x(k+N);u'(k+N);θ(k+N-1);...;θ(k+N-q)] (8)
将该输入参数α(k+N)代入公式(6)中,即可获得k+N时刻的参数变量θ(k+N)。
在本发明实施例中,利用单隐藏层神经网络对未知参数进行建模与估计,较好的解决了线性变参数***预测控制中的模型失配问题。该神经网络结构简单,训练速度快,避免了传统神经网络复杂的迭代训练,提高了计算效率。
在S120中,通过单层递归神经网络算法在线求解二次规划问题,根据该状态变量x(k)、该控制变量u(k-1)和该参数变量θ(k),确定满足该预测模型性能指标的控制增量Δu(k)。具体地,对于如公式(1)表示的被控***,可以定义k时刻至k+N时刻的几个参数,如下面的公式(9)所示:
其中,矩阵为k+1时刻至k+N时刻的状态变量x(k+1)至x(k+N)构成的矩阵;矩阵为k时刻至k+N-1时刻的控制变量u(k)至u(k+N-1)构成
的矩阵;矩阵为k时刻至k+N-1时刻的控制增量Δu(k)至Δu(k+N-1)构成的矩阵,对于任意一个控制增量Δu(k+j),可以表示为如公式(10)所示:
Δu(k+j)=u(k+j)-u(k+j-1) (10)
则根据公式(9)和公式(10),可以将公式(1)表示为下面的公式(11)所示:
其中,矩阵S、V和M分别表示为如下面的公式(12)所示:
其中,A(θ(·))为关于θ(·)的第一参考函数,B(θ(·))为关于θ(·)的第二参考函数,与被控对象有关;θ(·)可以为S110中确定的各个时刻的参数变量。
在本发明实施例中,将MPC的性能指标表示为如下面的公式(13)所示:
其中,Q和R为任意的正定对角矩阵,可以由用户进行定义选择,而P满足下面的不等式(14):
Q+KTRK+(A(θ(k+N))+B(θ(k+N))K)TP(A(θ(k+N))+B(θ(k+N))K)-P≤0
P>0 (14)
其中,K为辅助变量。
将公式(11)代入公式(13)可获得被控对象性能指标的约束优化问题,可以如下面的公式(15)表示:
其中,各个参数还满足下面的公式(16):
其中,和分别为S、V和M的后n行构成的矩阵,n为状态变量x(k)的维度,和表示预测模型的控制变量最大值和最小值,和表示预测模型的状态变量最大值和最小值,和表示预测模型的控制增量最大值和最小值,为n*n的单位矩阵。
如下面的公式(17)定义几个矩阵形式:
则根据公式(17),如公式(15)所示的性能指标可以表示为下面的公式(18)所示:
则相应的公式(17)可以表示为如公式(19)所示:
通过设计单层递归神经网络,可以在线求解二次规划问题,即可以在线求解约束优化问题,该神经网络的模型和自学习法可以由下面的公式(20)
定义,即根据下面的公式(20)确定公式(9)中k时刻至k+N-1时刻的控制增量
其中,λ是一个足够大的正实数,其具体数值可以由用户定义。通过最优化理论和神经动力学相关理论,该神经网络可以从任意初始状态收敛到对应约束优化问题的全局最优解。
在本发明实施例中,可以通过上述公式(20)确定k时刻至k+N-1时刻的控制增量例如,对于k时刻的控制增量Δu(k),则可以令N=1,代入上述的公式(20)中,则可以获得当前时刻k时刻的控制增量Δu(k),本发明并不限于此,根据N的取值的不同,可以确定当前时刻k时刻以及之后任意N个时刻中每个时刻的控制增量。
在本发明实施例中,利用递归神经网络在线计算最优控制变量,即最优控制信号,计算效率高,实时性好。并且,该神经网络的神经元数目与学习算法定量定性给出,实施起来简单方便,无需人为调整内部参数。
在S130中,根据该预测模型的该控制变量u(k-1)和该控制增量Δu(k),确定该预测模型在该k时刻的控制变量u(k),其中,u(k)=u(k-1)+Δu(k)。具体地,对于S130中确定的k时刻至k+N-1时刻的控制增量例如,对于k时刻的控制增量Δu(k),由于满足公式(9),因此将确定的控制增量Δu(k)与获得的前一时刻k-1时刻的控制变量u(k-1)求和,则可以获得当前时刻的控制变量u(k),依次类推,可以获得对于k+N-1时刻的控制增量将该控制增量与前一时刻k+N-2的控制变量u(k+N-2)求和,则可以获得k+N-1时刻的控制变量u(k+N-1),本发明并不限于此。
在本发明实施例中,将k+N-1时刻的控制变量u(k+N-1)和实时测量获得的状态变量x(k+N-1)代入公式(7)中,则可以获得k+N时刻的状态变量x(k+N),依次类推,获得k时刻以及k时刻之后任意时刻的状态变量以及控制变量,本发明并不限于此。
在S140中,根据该预测模型的该控制变量u(k),进行模型预测控制。
应理解,在本发明的各种实施例中,上述各过程的序号的大小并不意味着执行顺序的先后,各过程的执行顺序应以其功能和内在逻辑确定,而不应对本发明实施例的实施过程构成任何限定。
因此,本发明实施例的模型预测控制的方法,根据当前时刻k时刻的状态变量x(k)和参数变量θ(k),以及前一时刻k-1时刻的控制变量u(k-1),通过单层递归神经网络算法,确定满足预测模型性能指标的控制增量Δu(k),该控制增量Δu(k)与k-1时刻的控制变量u(k-1)的和为当前时刻k时刻的控制变量u(k),最后根据该控制变量u(k),进行模型预测控制。因此能够获得较现有技术更为优化的当前时刻控制变量,从而能够提高计算效率,从理论上保证了性能指标的准确度,即使得闭环控制***是渐进稳定的,并且整个模型预测控制***高度自主运行,实现了自动化操作。
下面将以质量弹簧***的MPC过程为例进行举例说明。具体地,由被控***的自身物理学运动规律可知,可以将预测模型写作如下面的公式(21)所示:
x(k+1)=A(θ(k))x(k))+Bu(k)) (21)
即对于如公式(1)的被控对象模型的一般表示形式,在质量弹簧***中可以写作如公式(21)所示的形式,其中,第一参考函数A(θ(k))和第二参考函数B的具体形式如下面的公式(22)所示:
在该质量弹簧***中,假设测量***的初始状态得到x(0)=[1;1;0;0];控制目标为将***状态变量镇定到零点;该状态变量可以为速度或加速度等,控制变量可以为施加的外力,但本发明并不限于此。具体地,本发明实施例的控制方法在该质量弹簧***上的实施过程如下:
首先,根据公式(9),定义从当前时刻k时刻到未来k+20时刻的几个未知参数,如公式(23)所示:
其中,矩阵为k+1时刻至k+20时刻的状态变量x(k+1)至x(k+20)构成的矩阵;矩阵为k时刻至k+19时刻的控制变量u(k)至u(k+19)构成的矩阵;矩阵为k时刻至k+19时刻的控制增量Δu(k)至Δu(k+19)构
成的矩阵,对于任意一个控制增量Δu(k+j),可以表示为如公式(10)所示。
第二,根据公式(11)将公式(21)进行变换,则根据公式(12)定义的参数矩阵S、V和M可以写成如下面的公式(24)所示:
其中,A(θ(k+i))满足下面的公式(25):
第三,构建单隐藏层神经网络,确定参数变量θ(k)。具体地,根据公式(3)定义输入参数α(k),这里,令q=1,获取当前时刻k时刻的状态变量x(k),预测k时刻的控制变量为u'(k),则可以确定输入参数α(k)表示为如公式(26)所示:
α(k)=[x(k);u'(k);θ(k-1)] (26)
首先,在被控***,即该质量弹簧***中,实测得到2000组样本数据,该样本数据包括2000组输入数据α=[α1,…,α2000]的具体数值和2000组对应的输出数据θ=[θ1,…,θ2000]的具体数值。
其次,设计一个单隐藏层神经网络,根据被控***的状态与输入数据的维度,令输入层的神经元数为6;设定隐藏层的数目为1000,可以由用户定
义;输出层的神经元数目为1。
再次,随机产生输入层到隐藏层的权值向量wi,神经元的偏置向量为bi。令每个神经元的激励函数g(·)=sin(·),将上述各个参数代入公式(4)中,可以获得神经元矩阵H。将矩阵H以及2000组样本数据的输出数据θ=[θ1,…,θ2000]代入公式(5)中,确定输出层权重参数β;再将该β代入公式(6)中,可以获得关于α的单隐藏层神经网络的模型函数θ(α)。
最后,将公式(26)确定的输入参数α(k)代入确定的单隐藏层神经网络的模型函数θ(α)中,即可获得参数变量θ(k)。
第四,将当前时刻k时刻的状态变量x(k)、获得的参数变量θ(k)以及预测的控制变量u'(k)代入公式(21)及(22),则可以获得k+1时刻的状态变量x(k+1)。更新公式(26)中的输入参数,获得k+1时刻的输入参数α(k+1)如下面公式(27)所示:
α(k+1)=[x(k+1);u'(k+1);θ(k)] (27)
将输入参数α(k+1)代入确定的单隐藏层神经网络的模型函数θ(α)中,即可对应的获得参数变量θ(k+1)。循环该步骤,即还可以依次获得参数变量θ(k+2);…θ(k+19)。
将上面获得的参数变量θ(k);…θ(k+19)依次代入公式(24)中,则可以分别获得参数矩阵S、V和M的数值。
第五,令Q和R矩阵为单位矩阵,将上述求得各个参数代入不等式(14)中,可以获得矩阵P,具体地,该P矩阵的具体表达式见下面的公式(28):
第六,根据公式(15)所描述的优化问题,将上述确定的参数矩阵S、V和M的数值代入公式(17)中,获得W、p、E和b的具体数值。
可选地,在第七步中,可以根据公式(20)先确定当前时刻k时刻的控
制增量Δu(k),并进而确定k时刻的最优控制变量u(k);令k=k+1,更新k的值,重复上述步骤中第三至第七步骤,直到k值取到控制时间的终点,例如k=k+10为止,但本发明并不限于此。
在本发明实施例中,采用上述方法对质量弹簧***进行控制,计算得到的控制变量u(·)如图3中的实线所示,虚线为通过现有技术的线性二次型调节器(linear quadratic regulator,简称“LQR”)确定的控制变量u(·)。另外,对应的,根据该控制变量对被控***进行控制,则如图4所示,实线为采用本发明实施例而获得的状态变量与时间的变化曲线x(k),虚线为采用LQR确定的状态变量与时间的曲线x(k)。
根据图4可知,通过本发明实施例获得的状态变量比LQR更快趋于零,也就是本发明实施例的方法使得该弹簧***更快镇定到零点状态,效果明显比LQR好。
应理解,在本发明的各种实施例中,上述各过程的序号的大小并不意味着执行顺序的先后,各过程的执行顺序应以其功能和内在逻辑确定,而不应对本发明实施例的实施过程构成任何限定。
因此,本发明实施例的模型预测控制的方法,根据当前时刻k时刻的状态变量x(k)和参数变量θ(k),以及前一时刻k-1时刻的控制变量u(k-1),通过单层递归神经网络算法,确定满足预测模型性能指标的控制增量Δu(k),该控制增量Δu(k)与k-1时刻的控制变量u(k-1)的和为当前时刻k时刻的控制变量u(k),最后根据该控制变量u(k),进行模型预测控制。因此能够获得相较于现有技术更为优化的当前时刻的控制变量,还能够提高计算效率,从理论上保证了性能指标的准确度,使得闭环控制***是渐进稳定的,并且整个模型预测控制***高度自主运行,实现了自动化操作。
下面将以一个数据中心的通风和空调***为例进行举例说明如何运用本发明的模型预测控制的方法来优化数据中心的温度与湿度。具体地,令Wz表示室内温度,Tz表示室内温度,Tsec表示次级线圈温度,表示空气流入的速率,则控制***的状态向量可以表示为根据先验知识建模可以得到控制模型如公式(1)所示,其中A(θ(k))和B(θ(k))如下面的公式(29)所示:
其中,Vz为区体积(zone volume),Wpri为主空气湿度(moisture content of the primary air),Wz,op为区湿度(zone moisture content),τv是阀门的时间常量(time constant of the valve),ε是增益常量(gain consant)。
另外,令u=[ρ;Tz,in],其中,ρ为开关阀门的打开幅度,Tz,in为进口冷冻水的温度。假设数据中心当前的温度时25度,湿度为10.25*10-3,控制目标为将室内温度变为24度,湿度变为9.25*10-3,则本发明实施例的控制方法的具体实施过程如下:
首先,根据公式(9),令N=10,定义从当前时刻k时刻到未来的k+10时刻的几个未知向量,如公式(30)所示:
其中,矩阵为k+1时刻至k+10时刻的状态变量x(k+1)至x(k+20)构成的矩阵;矩阵为k时刻至k+9时刻的控制变量u(k)至u(k+19)构成的矩阵;矩阵为k时刻至k+9时刻的控制增量Δu(k)至Δu(k+19)构成的矩阵,对于任意一个控制增量Δu(k+j),可以表示为如公式(10)所示。
第二,将公式(10)和公式(30)代入公式(1)中,则可以得到公式(11)中,其中参数矩阵S、V和M可以写成如公式(12)所示。
第三,构建单隐藏层神经网络,确定参数变量θ(k),其中,
θ(k)=[θ1(k);θ2(k);θ3(k);θ4(k);θ5(k)]。具体地,根据公式(3)定义输入参数α(k),这里,令q=1,获取当前时刻k时刻的状态变量x(k),预测k时刻的控制变量为u'(k),则可以确定输入参数α(k)表示为如公式(31)所示:
α(k)=[x(k);u'(k);θ(k-1)] (31)
首先,为了精确估计θ(k),对数据中心的通风和空调***进行离线数据采集,可以在2000个时刻进行采样从而得到2000组样本数据,即2000组输入数据α=[α1,…,α2000]的具体数值和2000组对应的输出数据θ=[θ1,…,θ2000]的具体数值。
其次,设计一个单隐藏层神经网络,根据被控***的状态与输入数据的维度,可以令输入层的神经元数为4+2+5=11;设定隐藏层神经元的数目为1000,可以由用户定义;输出层的神经元数目为5。
再次,随机产生输入层到隐藏层的权值向量wi,神经元的偏置向量为bi。令每个神经元的激励函数g(s)=tanh(s),将上述各个参数代入公式(4)中,可以获得神经元矩阵H。将矩阵H以及2000组样本数据的输出数据θ=[θ1,…,θ2000]代入公式(5)中,确定输出层权重参数β;再将该β代入公式(6)中,可以获得关于α的单隐藏层神经网络的模型函数θ(α)。
最后,将根据公式(31)确定的输入参数α(k)代入确定的单隐藏层神经网络的模型函数θ(α)中,即可获得参数变量θ(α(k)),即可以根据α(k)对应获得θ(α(k))。
第四,令当前k时刻为k=0时刻,测得***的状态变量x(k)=x(0)=[0.001;0.012;1;5],初始的控制变量为u(k)=u(0)=[0;0],则可以根据公式(31),依次以α(k);α(k+1);…;α(k+9)为输入信号,代入关于α(k)的单隐藏层神经网络的模型函数θ(α(k))中,即可相应地计算得到输出信号θ(k);θ(k+1);…;θ(k+9)。
将上面获得的参数变量θ(k);θ(k+1);…;θ(k+9)依次代入公式(12)中,则可以分别获得参数矩阵S、V和M的具体数值。
第五,令Q和R矩阵如下面的公式(32)所示:
将确定的Q、R、K、A(θ(k))和B(θ(k))等参数代入不等式(14)中,可以获得矩阵P,具体地,最后计算该P矩阵的具体表达式见下面的公式(33):
则相应的的公式(17)可以简化为如公式(35)所示:
根据公式(35)即可获得W、p、E和b的具体数值。
可选地,在第七步中,可以根据公式(20)先确定当前时刻k时刻的控制增量Δu(k),并进而确定k时刻的最优控制变量u(k);令k=k+1,更新k的值,重复上述步骤中第三至第七步骤,直到k值取到控制时间的终点,例如k=k+9为止,但本发明并不限于此。
应理解,在本发明的各种实施例中,上述各过程的序号的大小并不意味着执行顺序的先后,各过程的执行顺序应以其功能和内在逻辑确定,而不应对本发明实施例的实施过程构成任何限定。
因此,本发明实施例的模型预测控制的方法,根据当前时刻k时刻的状态变量x(k)和参数变量θ(k),以及前一时刻k-1时刻的控制变量u(k-1),通过单层递归神经网络算法,确定满足预测模型性能指标的控制增量Δu(k),
该控制增量Δu(k)与k-1时刻的控制变量u(k-1)的和为当前时刻k时刻的控制变量u(k),最后根据该控制变量u(k),进行模型预测控制。因此能够获得相较于现有技术更为优化的当前时刻的控制变量,还能够提高计算效率,从理论上保证了性能指标的准确度,使得闭环控制***是渐进稳定的,并且整个模型预测控制***高度自主运行,实现了自动化操作。
上文中结合图1至图4,详细描述了根据本发明实施例的模型预测控制的方法,下面将结合图5,描述根据本发明实施例的模型预测控制的装置。
图5示出了根据本发明实施例的模型预测控制的装置200的示意性框图,可选地,该模型预测控制的装置200中的各个模块可以集成在用一个芯片中,例如在神经形态计算芯片上可以包括该模型预测控制的装置200中各个模块。如图5所示,根据本发明实施例的模型预测控制的装置200包括:
第一确定模块210,用于根据预测模型在k-1时刻的至k-q时刻的参数变量θ(k-1)至θ(k-q)、在k时刻的状态变量x(k)以及在该k-1时刻的控制变量u(k-1)中的至少一个,确定在该k时刻的参数变量θ(k);
第二确定模块220,用于通过单层递归神经网络算法,根据该状态变量x(k)、该控制变量u(k-1)和该第一确定模块确定的该参数变量θ(k),确定满足该预测模型性能指标的控制增量Δu(k);
第三确定模块230,用于根据该预测模型的该控制变量u(k-1)和该第二确定模块确定的该控制增量Δu(k),确定该预测模型在该k时刻的控制变量u(k),其中,u(k)=u(k-1)+Δu(k);
控制模块240,用于根据该第三确定模块确定的该预测模型的该控制变量u(k),进行模型预测控制。
因此,本发明实施例的模型预测控制的装置,根据当前时刻k时刻的状态变量x(k)和参数变量θ(k),以及前一时刻k-1时刻的控制变量u(k-1),通过单层递归神经网络算法,确定满足预测模型性能指标的控制增量Δu(k),该控制增量Δu(k)与k-1时刻的控制变量u(k-1)的和为当前时刻k时刻的控制变量u(k),最后根据该控制变量u(k),进行模型预测控制。因此能够获得相较于现有技术更为优化的当前时刻的控制变量,还能够提高计算效率,从理论上保证了性能指标的准确度,使得闭环控制***是渐进稳定的,并且整个模型预测控制***高度自主运行,实现了自动化操作。
在本发明实施例中,第一确定模块210可以根据预测模型在k-1时刻的
至k-q时刻的参数变量θ(k-1)至θ(k-q)、在k时刻的状态变量x(k)以及在该k-1时刻的控制变量u(k-1)中的至少一个,确定在该k时刻的参数变量θ(k)。具体地,对于被控对象的模型可以表示为如公式(1)所示,其中,被控对象当前时刻k时刻的状态变量以及k时刻的前一时刻k-1时刻的控制变量,可以通过测量实时获取得到;而参数变量θ(k)可以根据预测模型在k-1时刻的至k-q时刻的参数变量θ(k-1)至θ(k-q)、在k时刻的状态变量x(k)以及在该k-1时刻的控制变量u(k-1)中的至少一个由第一确定模块210确定,具体地,可以利用现有技术确定该参数变量θ(k),也可以通过本发明实施例中单隐藏层神经网络确定该参数变量θ(k),本发明并不限于此。
可选地,第一确定模块210可以通过单隐藏层神经网络对该参数变量θ(k)进行建模和在线估计。神经网络是一种模拟人脑结构行为特征进行分布式并行信息处理的计算模型。神经网络依靠其学习算法调整其内部大量神经元之间的相互连接关系,从而达到特定的计算目的。该第一确定模块210可以为一个专用的处理器,该处理器可以包括多个单元,如矩阵乘积单元,矩阵求逆单元,随机数生成单元,非线性函数映射单元和存储单元等。具体地,该处理器的操作可以包括离线训练和在线预测两种模式,离线训练模式主要用于确定处理器里每个单元的配置和函数关系,例如确定单隐藏层神经网络的模型函数θ(α);而在线预测模式主要用于根据离线训练结果,通过一定的输入数据,确定相应的输出数据,例如用于确定k时刻的参数变量θ(k),但本发明并不限于此。
在本发明实施例中,首先可以由第一确定模块210确定单隐藏层神经网络的模型函数θ(α),具体地,可以先通过公式(2)定义一个输入参数α(k),即对于当前时刻的参数变量θ(k),可以表示为一个关于输入参数α(k)的函数F(α(k)),由于该函数的输入为α(k),输出为参数变量θ(k),即可以表示为一个模型函数θ(α),其中输入参数α(k)满足公式(3),其中,x(k)为当前时刻k时刻的状态变量;u'(k)为当前时刻的控制变量的预测量,即预测控制变量;k-1时刻至k-q时刻的参数变量为θ(k-1)至θ(k-q),其中q为时间常数,可以由用户进行定义。
具体地,可以通过第一确定模块210在离线训练模式下,通过下面的方法确定该单隐藏层神经网络的模型函数θ(α)的具体形式。首先对被控对象进行离线分析,可以获得两组数据θ=[θ1,…,θs]以及α=[α1,…,αs],其中s是样
本数据的数量,由用户进行定义,样本数量越大,准确度越高,但是采样成本越高,因此可以根据经验值确定合理的样本数量。另外,这里的每个α和θ一一对应,即对于每个输入αi,对应地可以获得一个输出θi。
如图2所示,构建单隐藏层神经网络。该单隐藏层神经网络的输入层神经元数目为n+m+pq,n为状态变量x(k)的维度,m为控制变量u(k)的维度;输出层神经元数目为p,p为θ(k)的维度;隐藏层神经元的数目为L,L的值可以由用户进行定义;隐藏层神经元激励函数为g(·),g(·)可以由经验值确定;第i个输入层到隐藏层的权值向量为wi,神经元的偏置向量为bi,wi和bi可以随机产生。
将样本中的输入参数α=[α1,…,αs]代入公式(4)中,获得神经元矩阵H。将获得的矩阵H以及s个样本中的输出θ=[θ1,…,θs]代入公式(5)中,获得该单隐藏层神经网络神经元与输出层相连的权重参数β,则可以确定完成训练的该单隐藏层神经网络的模型函数θ(α)表示为公式(6),其中,βi为权重参数β的矩阵的第i行。
因此,对于当前时刻k时刻,以公式(3)定义的输入参数α(k)为输入,代入公式(6)中,即可获得k时刻的参数变量θ(k)。
在本发明实施例中,当第一确定模块210确定了k时刻的参数变量θ(k)后,可以代入公式(1)中,可以确定k+1时刻的状态变量x(k+1),再根据k+1时刻的预测的控制变量u'(k+1),可以确定k+1时刻的参数变量θ(k+1),依次类推,对于确定任意时刻k+N时刻的参数变量θ(k+N),首先根据k时刻的参数变量θ(k)以及k+N-1时刻的预测控制变量u'(k+N-1),通过公式(7),可以获得k+N时刻的状态变量x(k+N),其中,该公式(7)为公式(1)在时刻k+N时刻的变形形式,A(θ(·))为关于θ(·)的第一参考函数,B(θ(·))为关于θ(·)的第二参考函数,N为正整数。
对于确定的k+N时刻的状态变量x(k+N)以及k+N时刻的预测控制变量u(k+N),可以类似的通过公式(3)确定输入参数α(k+N)如公式(8)所示,将该输入参数α(k+N)代入公式(6)中,即可获得k+N时刻的参数变量θ(k+N)。
在本发明实施例中,利用单隐藏层神经网络对未知参数进行建模与估计,较好的解决了线性变参数***预测控制中的模型失配问题。该神经网络结构简单,训练速度快,避免了传统神经网络复杂的迭代训练,提高了计算效率。
在本发明实施例中,第二确定模块220通过单层递归神经网络算法,根据该状态变量x(k)、该控制变量u(k-1)和第一确定模块210该参数变量θ(k),确定满足该预测模型性能指标的控制增量Δu(k)。可选地,该第二确定模块220,也可以为递归神经网络模块,可以由一个专用处理器组成,该处理器可以包括矩阵乘积单元,矩阵求和单元,max函数运算单元和随机数生成单元等多个单元。
具体地,对于如公式(1)表示的被控***,该第二确定模块220可以定义k时刻至k+N时刻的几个参数,如公式(9)所示,其中,矩阵x(k)为k+1时刻至k+N时刻的状态变量x(k+1)至x(k+N)构成的矩阵;矩阵u(k)为k时刻至k+N-1时刻的控制变量u(k)至u(k+N-1)构成的矩阵;矩阵Δu(k)为k时刻至k+N-1时刻的控制增量Δu(k)至Δu(k+N-1)构成的矩阵,对于任意一个控制增量Δu(k+j),可以表示为如公式(10)所示。根据公式(9)和公式(10),可以将公式(1)表示为如公式(11)所示,其中,矩阵S、V和M分别表示为如公式(12)所示,其中,A(θ(·))为关于θ(·)的第一参考函数,B(θ(·))为关于θ(·)的第二参考函数,与被控对象有关;θ(·)可以为第一确定模块210确定的各个时刻的参数变量。
在本发明实施例中,将MPC的性能指标表示为如公式(13)所示,其中,Q和R为任意的正定对角矩阵,可以由用户进行定义选择,而P满足不等式(14),其中,K为辅助变量。
将公式(11)代入公式(13)可获得被控对象性能指标的约束优化问题,可以如公式(15)表示,其中,各个参数还满足公式(16),其中,和分别为S、V和M的后n行构成的矩阵,n为状态变量x(k)的维度,和表示预测模型的控制变量最大值和最小值,和表示预测模型的状态变量最大值和最小值,和表示预测模型的控制增量最大值和最小值,为n*n的单位矩阵。
则根据公式(17),如公式(15)所示的性能指标可以表示为公式(18)所示,则相应的公式(17)可以表示为如公式(19)所示。
在本发明实施例中,第二确定模块220通过设计单层递归神经网络,可
以在线求解约束优化问题,该神经网络的模型和自学习法可以由公式(20)定义,即根据公式(20)确定公式(9)中k时刻至k+N-1时刻的控制增量其中,λ是一个足够大的正实数,其具体数值可以由用户定义。通过最优化理论和神经动力学相关理论,该神经网络可以从任意初始状态收敛到对应约束优化问题的全局最优解。
在本发明实施例中,可以通过上述公式(20)确定k时刻至k+N-1时刻的控制增量例如,对于k时刻的控制增量Δu(k),则可以令N=1,代入上述的公式(20)中,则可以获得当前时刻k时刻的控制增量Δu(k),本发明并不限于此,根据N的取值的不同,可以确定当前时刻k时刻以及之后任意N个时刻中每个时刻的控制增量。
在本发明实施例中,利用递归神经网络在线计算最优控制变量,即最优控制信号,计算效率高,实时性好。并且,该神经网络的神经元数目与学习算法定量定性给出,实施起来简单方便,无需人为调整内部参数。
在本发明实施例中,第三确定模块230根据该预测模型的该控制变量u(k-1)和该控制增量Δu(k),确定该预测模型在该k时刻的控制变量u(k),其中,u(k)=u(k-1)+Δu(k)。具体地,对于到第二确定模块220中确定的k时刻至k+N-1时刻的控制增量例如,对于k时刻的控制增量Δu(k),由于满足公式(9),因此将确定的控制增量Δu(k)与获得的前一时刻k-1时刻的控制变量u(k-1)求和,则可以获得当前时刻的控制变量u(k),依次类推,第三确定模块230可以计算获得对于k+N-1时刻的控制增量将该控制增量与前一时刻k+N-2的控制变量u(k+N-2)求和,则可以获得k+N-1时刻的控制变量u(k+N-1),本发明并不限于此。
在本发明实施例中,将k+N-1时刻的控制变量u(k+N-1)和实时测量获得的状态变量x(k+N-1)代入公式(7)中,则可以获得k+N时刻的状态变量x(k+N),依次类推,获得k时刻以及k时刻之后任意时刻的状态变量以及控制变量,本发明并不限于此。
在本发明实施例中,控制模块240根据第三确定模块230确定的该预测模型的该控制变量u(k),进行模型预测控制。
应理解,根据本发明实施例的模型预测控制的装置200可对应于执行本发明实施例中的模型预测控制的方法100,并且模型预测控制的装置200中的各个模块的上述和其它操作和/或功能分别为了实现图1至图2中的各个
方法的相应流程,为了简洁,在此不再赘述。
因此,本发明实施例的模型预测控制的装置,根据当前时刻k时刻的状态变量x(k)和参数变量θ(k),以及前一时刻k-1时刻的控制变量u(k-1),通过单层递归神经网络算法,确定满足预测模型性能指标的控制增量Δu(k),该控制增量Δu(k)与k-1时刻的控制变量u(k-1)的和为当前时刻k时刻的控制变量u(k),最后根据该控制变量u(k),进行模型预测控制。因此能够获得相较于现有技术更为优化的当前时刻的控制变量,还能够提高计算效率,从理论上保证了性能指标的准确度,使得闭环控制***是渐进稳定的,并且整个模型预测控制***高度自主运行,实现了自动化操作。
如图6所示,本发明实施例还提供了一种模型预测控制的装置300,包括处理器310、存储器320和总线***330。其中,处理器310和存储器320通过总线***330相连,该存储器320用于存储指令,该处理器310用于执行该存储器320存储的指令。该存储器320存储程序代码,且处理器310可以调用存储器320中存储的程序代码执行以下操作:根据预测模型在k-1时刻的至k-q时刻的参数变量θ(k-1)至θ(k-q)、在k时刻的状态变量x(k)以及在该k-1时刻的控制变量u(k-1)中的至少一个,确定在该k时刻的参数变量θ(k);通过单层递归神经网络算法,根据该状态变量x(k)、该控制变量u(k-1)和该参数变量θ(k),确定满足该预测模型性能指标的控制增量Δu(k);根据该预测模型的该控制变量u(k-1)和该控制增量Δu(k),确定该预测模型在该k时刻的控制变量u(k),其中,u(k)=u(k-1)+Δu(k);根据该预测模型的该控制变量u(k),进行模型预测控制。
因此,本发明实施例的模型预测控制的装置,根据当前时刻k时刻的状态变量x(k)和参数变量θ(k),以及前一时刻k-1时刻的控制变量u(k-1),通过单层递归神经网络算法,确定满足预测模型性能指标的控制增量Δu(k),该控制增量Δu(k)与k-1时刻的控制变量u(k-1)的和为当前时刻k时刻的控制变量u(k),最后根据该控制变量u(k),进行模型预测控制。因此能够获得相较于现有技术更为优化的当前时刻的控制变量,还能够提高计算效率,从理论上保证了性能指标的准确度,使得闭环控制***是渐进稳定的,并且整个模型预测控制***高度自主运行,实现了自动化操作。
应理解,在本发明实施例中,该处理器310可以是中央处理单元(Central Processing Unit,简称为“CPU”),该处理器310还可以是其他通用处理器、
数字信号处理器(DSP)、专用集成电路(ASIC)、现成可编程门阵列(FPGA)或者其他可编程逻辑器件、分立门或者晶体管逻辑器件、分立硬件组件等。通用处理器可以是微处理器或者该处理器也可以是任何常规的处理器等。
该存储器320可以包括只读存储器和随机存取存储器,并向处理器310提供指令和数据。存储器320的一部分还可以包括非易失性随机存取存储器。例如,存储器320还可以存储设备类型的信息。
该总线***330除包括数据总线之外,还可以包括电源总线、控制总线和状态信号总线等。但是为了清楚说明起见,在图中将各种总线都标为总线***330。
在实现过程中,上述方法的各步骤可以通过处理器310中的硬件的集成逻辑电路或者软件形式的指令完成。结合本发明实施例所公开的方法的步骤可以直接体现为硬件处理器执行完成,或者用处理器中的硬件及软件模块组合执行完成。软件模块可以位于随机存储器,闪存、只读存储器,可编程只读存储器或者电可擦写可编程存储器、寄存器等本领域成熟的存储介质中。该存储介质位于存储器320,处理器310读取存储器320中的信息,结合其硬件完成上述方法的步骤。为避免重复,这里不再详细描述。
可选地,作为一个实施例,处理器310可以调用存储器320中存储的程序代码执行以下操作:确定单隐藏层神经网络的模型函数θ(α);根据该预测模型的该状态变量x(k)、在该k时刻的预测控制变量u'(k)以及该k-1时刻至该k-q时刻的该参数变量θ(k-1)至θ(k-q),确定输入参数α(k)=[x(k);u'(k);θ(k-1);...;θ(k-q)],其中,q为整数,1≤q<k;将该输入参数α(k)代入该模型函数θ(α)中,计算得到该k时刻的该参数变量θ(k)。
可选地,作为一个实施例,处理器310可以调用存储器320中存储的程序代码执行以下操作:根据该k时刻的该参数变量θ(k)、该状态变量x(k)以及k+N-1时刻的预测控制变量u'(k+N-1),通过公式(7),确定该预测模型在k+N时刻的该状态变量x(k+N),其中A(θ(·))为关于θ(·)的第一参考函数,B(θ(·))为关于θ(·)的第二参考函数,N为时间步长,N为正整数;根据该状态变量x(k+N)、在该k+N时刻的预测控制变量u'(k+N)以及k+N-1时刻至k+N-q时刻的参数变量θ(k+N-1)至θ(k+N-q),确定输入参数α(k+N)=[x(k+N);u'(k+N);θ(k+N-1);...;θ(k+N-q)],其中,q为整数,1≤q<k;将该输入参数α(k+N)代入该模型函数θ(α)中,计算得到该k+N时
刻的该参数变量θ(k+N)。
可选地,作为一个实施例,处理器310可以调用存储器320中存储的程序代码执行以下操作:确定s组输入数据α=[α1,…,αs]和对应的s组输出数据θ=[θ1,…,θs];构建该单隐藏层神经网络,该单隐藏层神经网络的输入层神经元数目为n+m+pq,隐藏层神经元的数目为L,输出层神经元数目为p,隐藏层神经元激励函数为g(·),第i个输入层到隐藏层的权值向量为wi,神经元的偏置向量为bi,其中,n为该状态变量x(k)的维度,m为该控制变量u(k)的维度;根据该单隐藏层神经网络、该输入数据α=[α1,…,αs]和该输出数据θ=[θ1,…,θs],确定该单隐藏层神经网络神经元与输出层相连的权重参数β=HT(I+HHT)-1[θ1,...,θs],其中H满足公式(4),确定该模型函数θ(α)如公式(5)所示,其中,βi为该权重参数β的第i行。
可选地,作为一个实施例,处理器310可以调用存储器320中存储的程序代码执行以下操作:通过该单层递归神经网络算法,根据下面的公式确定该控制增量Δu(k):
A(θ(·))为关于θ(·)的第一参考函数,B(θ(·))为关于θ(·)的第二参考函数,和分别为S、V和M的后n行构成的矩阵,n为该状态变量x(k)的维度,[-umin+u(k-1)]为每一行均为-umin+u(k-1)的m行矩阵,
[umax-u(k-1)]为每一行均为umax-u(k-1)的m行矩阵,m为该控制变量u(k)的维度,λ为正实数,umax和umin表示该预测模型的控制变量最大值和最小值,xmax和xmin表示该预测模型的状态变量最大值和最小值,Q和R为任意正定对角矩阵,P满足下面的不等式:
Q+KTRK+(A(θ(k+1))+B(θ(k+1))K)TP(A(θ(k+1))+B(θ(k+1))K)-P≤0
其中,P>0,K为辅助变量。
可选地,作为一个实施例,处理器310可以调用存储器320中存储的程序代码执行以下操作:通过该单层递归神经网络算法,根据公式(20)确定该k时刻至k+N-1时刻的控制增量其中,矩阵S、V和M分别满足公式(12),矩阵W、p、E和b分别满足公式(17),Δu(k+j)=u(k+j)-u(k+j-1)],0≤j≤N,A(θ(·))为关于θ(·)的第一参考函数,B(θ(·))为关于θ(·)的第二参考函数,和分别为S、V和M的后n行构成的矩阵,n为该状态变量x(k)的维度,为每一行均为的m*N行矩阵,为每一行均为的m*N行矩阵,m为该控制变量u(k)的维度,N为时间步长,λ为正实数,和表示该预测模型的控制变量最大值和最小值,和表示该预测模型的状态变量最大值和最小值,Q和R为任意正定对角矩阵,P满足不等式(14),K为辅助变量。
可选地,作为一个实施例,处理器310可以调用存储器320中存储的程序代码执行以下操作:根据该k时刻至该k+N-1时刻的该控制增量以及该k-1时刻至k+N-2时刻的控制变量确定该k时刻至该k+N-1时刻的控制变量 其中, 根据该k时刻至该k+N-1时刻的控制变量进行模型预测控制。
应理解,根据本发明实施例的模型预测控制的装置300可对应于本发明实施例中的模型预测控制的装置200,并可以对应于执行根据本发明实施例的方法100中的相应主体,并且模型预测控制的装置300中的各个模块的上述和其它操作和/或功能分别为了实现图1至图2中的各个方法的相应流程,为了简洁,在此不再赘述。
因此,本发明实施例的模型预测控制的装置,根据当前时刻k时刻的状态变量x(k)和参数变量θ(k),以及前一时刻k-1时刻的控制变量u(k-1),通
过单层递归神经网络算法,确定满足预测模型性能指标的控制增量Δu(k),该控制增量Δu(k)与k-1时刻的控制变量u(k-1)的和为当前时刻k时刻的控制变量u(k),最后根据该控制变量u(k),进行模型预测控制。因此能够获得相较于现有技术更为优化的当前时刻的控制变量,还能够提高计算效率,从理论上保证了性能指标的准确度,使得闭环控制***是渐进稳定的,并且整个模型预测控制***高度自主运行,实现了自动化操作。
本领域普通技术人员可以意识到,结合本文中所公开的实施例描述的各示例的单元及算法步骤,能够以电子硬件、或者计算机软件和电子硬件的结合来实现。这些功能究竟以硬件还是软件方式来执行,取决于技术方案的特定应用和设计约束条件。专业技术人员可以对每个特定的应用来使用不同方法来实现所描述的功能,但是这种实现不应认为超出本发明的范围。
所属领域的技术人员可以清楚地了解到,为描述的方便和简洁,上述描述的***、装置和单元的具体工作过程,可以参考前述方法实施例中的对应过程,在此不再赘述。
在本申请所提供的几个实施例中,应该理解到,所揭露的***、装置和方法,可以通过其它的方式实现。例如,以上所描述的装置实施例仅仅是示意性的,例如,所述单元的划分,仅仅为一种逻辑功能划分,实际实现时可以有另外的划分方式,例如多个单元或组件可以结合或者可以集成到另一个***,或一些特征可以忽略,或不执行。另一点,所显示或讨论的相互之间的耦合或直接耦合或通信连接可以是通过一些接口,装置或单元的间接耦合或通信连接,可以是电性,机械或其它的形式。
所述作为分离部件说明的单元可以是或者也可以不是物理上分开的,作为单元显示的部件可以是或者也可以不是物理单元,即可以位于一个地方,或者也可以分布到多个网络单元上。可以根据实际的需要选择其中的部分或者全部单元来实现本实施例方案的目的。
另外,在本发明各个实施例中的各功能单元可以集成在一个处理单元中,也可以是各个单元单独物理存在,也可以两个或两个以上单元集成在一个单元中。
所述功能如果以软件功能单元的形式实现并作为独立的产品销售或使用时,可以存储在一个计算机可读取存储介质中。基于这样的理解,本发明的技术方案本质上或者说对现有技术做出贡献的部分或者该技术方案的部
分可以以软件产品的形式体现出来,该计算机软件产品存储在一个存储介质中,包括若干指令用以使得一台计算机设备(可以是个人计算机,服务器,或者网络设备等)执行本发明各个实施例所述方法的全部或部分步骤。而前述的存储介质包括:U盘、移动硬盘、只读存储器(ROM,Read-Only Memory)、随机存取存储器(RAM,Random Access Memory)、磁碟或者光盘等各种可以存储程序代码的介质。
以上所述,仅为本发明的具体实施方式,但本发明的保护范围并不局限于此,任何熟悉本技术领域的技术人员在本发明揭露的技术范围内,可轻易想到变化或替换,都应涵盖在本发明的保护范围之内。因此,本发明的保护范围应所述以权利要求的保护范围为准。
Claims (14)
- 一种模型预测控制的方法,其特征在于,所述方法包括:根据预测模型在k-1时刻的至k-q时刻的参数变量θ(k-1)至θ(k-q)、在k时刻的状态变量x(k)以及在所述k-1时刻的控制变量u(k-1)中的至少一个,确定在所述k时刻的参数变量θ(k);通过单层递归神经网络算法在线求解二次规划问题,根据所述状态变量x(k)、所述控制变量u(k-1)和所述参数变量θ(k),确定满足所述预测模型性能指标的控制增量Δu(k);根据所述预测模型的所述控制变量u(k-1)和所述控制增量Δu(k),确定所述预测模型在所述k时刻的控制变量u(k),其中,u(k)=u(k-1)+Δu(k);根据所述预测模型的所述控制变量u(k),进行模型预测控制。
- 根据权利要求1所述的方法,其特征在于,所述根据预测模型在k-1时刻的至k-q时刻的参数变量θ(k-1)至θ(k-q)、在k时刻的状态变量x(k)以及在所述k-1时刻的控制变量u(k-1)中的至少一个,确定在所述k时刻的参数变量θ(k),包括:确定单隐藏层神经网络的模型函数θ(α);根据所述预测模型的所述状态变量x(k)、在所述k时刻的预测控制变量u'(k)以及所述k-1时刻至所述k-q时刻的所述参数变量θ(k-1)至θ(k-q),确定输入参数α(k)=[x(k);u'(k);θ(k-1);...;θ(k-q)],其中,q为整数,1≤q<k;将所述输入参数α(k)代入所述模型函数θ(α)中,计算得到所述k时刻的所述参数变量θ(k)。
- 根据权利要求2所述的方法,其特征在于,所述确定单隐藏层神经网络的模型函数θ(α),包括:确定s组输入数据α=[α1,…,αs]和对应的s组输出数据θ=[θ1,…,θs];构建所述单隐藏层神经网络,所述单隐藏层神经网络的输入层神经元数目为n+m+pq,隐藏层神经元的数目为L,输出层神经元数目为p,隐藏层神经元激励函数为g(·),第i个输入层到隐藏层的权值向量为wi,神经元的偏置向量为bi,其中,n为所述状态变量x(k)的维度,m为所述控制变量u(k)的维度;根据所述单隐藏层神经网络、所述输入数据α=[α1,…,αs]和所述输出数据θ=[θ1,…,θs],确定所述单隐藏层神经网络神经元与输出层相连的权重参 数β=HT(I+HHT)-1[θ1,...,θs],其中:确定所述模型函数θ(α):其中,βi为所述权重参数β的第i行。
- 根据权利要求2或3所述的方法,其特征在于,所述方法还包括:根据所述k时刻的所述参数变量θ(k)、所述状态变量x(k)以及k+N-1时刻的预测控制变量u'(k+N-1),通过下面的公式,确定所述预测模型在k+N时刻的所述状态变量x(k+N):x(k+N)=A(θ(k+N-1))x(k+N-1))+B(θ(k+N-1))u'(k+N-1))其中A(θ(·))为关于θ(·)的第一参考函数,B(θ(·))为关于θ(·)的第二参考函数,N为时间步长,N为正整数;根据所述状态变量x(k+N)、在所述k+N时刻的预测控制变量u'(k+N)以及k+N-1时刻至k+N-q时刻的参数变量θ(k+N-1)至θ(k+N-q),确定输入参数α(k+N)=[x(k+N);u'(k+N);θ(k+N-1);...;θ(k+N-q)],其中,q为整数,1≤q<k;将所述输入参数α(k+N)代入所述模型函数θ(α)中,计算得到所述k+N时刻的所述参数变量θ(k+N)。
- 根据权利要求1至4中任一项所述的方法,其特征在于,所述通过单层递归神经网络算法在线求解二次规划问题,根据所述状态变量x(k)、所述控制变量u(k-1)和所述参数变量θ(k),确定满足所述预测模型性能指标的控制增量Δu(k),包括:通过所述单层递归神经网络算法,根据下面的公式确定所述控制增量Δu(k):A(θ(·))为关于θ(·)的第一参考函数,B(θ(·))为关于θ(·)的第二参考函数,和分别为S、V和M的后n行构成的矩阵,n为所述状态变量x(k)的维度,-umin+u(k-1)为每一行均为-umin+u(k-1)的m行矩阵,umax-u(k-1)为每一行均为umax-u(k-1)的m行矩阵,m为所述控制变量u(k)的维度,λ为正实数,umax和umin表示所述预测模型的控制变量最大值和最小值,xmax和xmin表示所述预测模型的状态变量最大值和最小值,Q和R为任意正定对角矩阵,P满足下面的不等式:Q+KTRK+(A(θ(k+1))+B(θ(k+1))K)TP(A(θ(k+1))+B(θ(k+1))K)-P≤0其中,P>0,K为辅助变量。
- 根据权利要求3或4所述的方法,其特征在于,所述方法还包括:Δu(k+j)=u(k+j)-u(k+j-1)],0≤j≤N,A(θ(·))为关于θ(·)的第一参考函数,B(θ(·))为关于θ(·)的第二参考函数,和分别为S、V和M的后n行构成的矩阵,n为所述状态变量x(k)的维度,为每一行均为的m*N行矩阵,为每一行均为的m*N行矩阵,m为所述控制变量u(k)的维度,N为时间步长,λ为正实数,表示所述预测模型的控制变量最大值和最小值,和表示所述预测模型的状态变量最大值和最小值,Q和R为任意正定对角矩阵,P满足下面的不等式:Q+KTRK+(A(θ(k+N))+B(θ(k+N))K)TP(A(θ(k+N))+B(θ(k+N))K)-P≤0其中,P>0,K为辅助变量。
- 一种模型预测控制的装置,其特征在于,所述装置包括:第一确定模块,用于根据预测模型在k-1时刻的至k-q时刻的参数变量θ(k-1)至θ(k-q)、在k时刻的状态变量x(k)以及在所述k-1时刻的控制变量u(k-1)中的至少一个,确定在所述k时刻的参数变量θ(k);第二确定模块,用于通过单层递归神经网络算法在线求解二次规划问题,根据所述状态变量x(k)、所述控制变量u(k-1)和所述第一确定模块确定的所述参数变量θ(k),确定满足所述预测模型性能指标的控制增量Δu(k);第三确定模块,用于根据所述预测模型的所述控制变量u(k-1)和所述第二确定模块确定的所述控制增量Δu(k),确定所述预测模型在所述k时刻的控制变量u(k),其中,u(k)=u(k-1)+Δu(k);控制模块,用于根据所述第三确定模块确定的所述预测模型的所述控制变量u(k),进行模型预测控制。
- 根据权利要求8所述的装置,其特征在于,所述第一确定模块具体用于:确定单隐藏层神经网络的模型函数θ(α);根据所述预测模型的所述状态变量x(k)、在所述k时刻的预测控制变量u'(k)以及所述k-1时刻至所述k-q时刻的所述参数变量θ(k-1)至θ(k-q),确定输入参数α(k)=[x(k);u'(k);θ(k-1);...;θ(k-q)],其中,q为整数,1≤q<k;将所述输入参数α(k)代入所述模型函数θ(α)中,计算得到所述k时刻的所述参数变量θ(k)。
- 根据权利要求9所述的装置,其特征在于,所述第一确定模块具体用于:确定s组输入数据α=[α1,…,αs]和对应的s组输出数据θ=[θ1,…,θs];构建所述单隐藏层神经网络,所述单隐藏层神经网络的输入层神经元数目为n+m+pq,隐藏层神经元的数目为L,输出层神经元数目为p,隐藏层神经元激励函数为g(·),第i个输入层到隐藏层的权值向量为wi,神经元的偏置向量为bi,其中,n为所述状态变量x(k)的维度,m为所述控制变量u(k)的维度;根据所述单隐藏层神经网络、所述输入数据α=[α1,…,αs]和所述输出数据θ=[θ1,…,θs],确定所述单隐藏层神经网络神经元与输出层相连的权重参数β=HT(I+HHT)-1[θ1,...,θs],其中:确定所述模型函数θ(α):其中,βi为所述权重参数β的第i行。
- 根据权利要求9或10所述的装置,其特征在于,所述第一确定模块具体用于:根据所述k时刻的所述参数变量θ(k)、所述状态变量x(k)以及k+N-1时刻的预测控制变量u'(k+N-1),通过下面的公式,确定所述预测模型在k+N时刻的所述状态变量x(k+N):x(k+N)=A(θ(k+N-1))x(k+N-1))+B(θ(k+N-1))u'(k+N-1))其中A(θ(·))为关于θ(·)的第一参考函数,B(θ(·))为关于θ(·)的第二参考函数,N为时间步长,N为正整数;根据所述状态变量x(k+N)、在所述k+N时刻的预测控制变量u'(k+N)以及k+N-1时刻至k+N-q时刻的参数变量θ(k+N-1)至θ(k+N-q),确定输入参数α(k+N)=[x(k+N);u'(k+N);θ(k+N-1);...;θ(k+N-q)],其中,q为整数,1≤q<k;将所述输入参数α(k+N)代入所述模型函数θ(α)中,计算得到所述k+N时刻的所述参数变量θ(k+N)。
- 根据权利要求8至11中任一项所述的装置,其特征在于,所述第二确定模块具体用于:通过所述单层递归神经网络算法,根据下面的公式确定所述控制增量Δu(k):A(θ(·))为关于θ(·)的第一参考函数,B(θ(·))为关于θ(·)的第二参考函数,和分别为S、V和M的后n行构成的矩阵,n为所述状态变量x(k)的维度,[-umin+u(k-1)]为每一行均为-umin+u(k-1)的m行矩阵,[umax-u(k-1)]为每一行均为umax-u(k-1)的m行矩阵,m为所述控制变量u(k)的维度,λ为正实数,umax和umin表示所述预测模型的控制变量最大值和最小值,xmax和xmin表示所述预测模型的状态变量最大值和最小值,Q和R为任意正定对角矩阵,P满足下面的不等式:Q+KTRK+(A(θ(k+1))+B(θ(k+1))K)TP(A(θ(k+1))+B(θ(k+1))K)-P≤0其中,P>0,K为辅助变量。
- 根据权利要求10或11所述的装置,其特征在于,所述第二确定模块还用于:Δu(k+j)=u(k+j)-u(k+j-1)],0≤j≤N,A(θ(·))为关于θ(·)的第一参考函数,B(θ(·))为关于θ(·)的第二参考函数,和分别为S、V和M的后n行构成的矩阵,n为所述状态变量x(k)的维度,为每一行均为的m*N行矩阵,为每一行均为的m*N行矩阵,m为所述控制变量u(k)的维度,N为时间步长,λ为正实数,和表示所述预测模型的控制变量最大值和最小值,和表示所述预测模型的状态变量最大值和最小值,Q和R为任意正定对角矩阵,P满足下面的不等式:Q+KTRK+(A(θ(k+N))+B(θ(k+N))K)TP(A(θ(k+N))+B(θ(k+N))K)-P≤0其中,P>0,K为辅助变量。
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