CN114839874A - Parallel control method and system for system model partial unknown - Google Patents

Parallel control method and system for system model partial unknown Download PDF

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CN114839874A
CN114839874A CN202210412304.3A CN202210412304A CN114839874A CN 114839874 A CN114839874 A CN 114839874A CN 202210412304 A CN202210412304 A CN 202210412304A CN 114839874 A CN114839874 A CN 114839874A
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刘德荣
林锦全
王永华
赵博
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Abstract

The invention provides a parallel control method and system facing to system model partial unknown, which comprises the steps of constructing an RBF neural network, approximating the unknown part of a system model by using the RBF neural network, and reconstructing the system model to obtain a reconstructed system model; constructing a sliding mode function according to the reconstruction system model; and constructing a parallel controller based on the RBF neural network and the sliding mode function, and controlling the system to run to a balanced state by using the parallel controller. The invention obtains a complete reconstruction system model by using the unknown part of the RBF neural network approximation system model, designs a corresponding parallel controller to control the system, effectively solves the problem that a control signal is difficult to generate when the system state cannot be obtained under the condition that the system model is partially unknown, and can be widely applied to the actual system with the partially unknown system model.

Description

Parallel control method and system for system model partial unknown
Technical Field
The invention relates to the field of intelligent control, in particular to a parallel control method and system facing to system model partial unknown.
Background
In today's industrial control systems, most system control problems are analyzed by a state feedback control method, i.e., the control problems of the system are analyzed by designing a state feedback controller to form a closed loop system and taking a control law as a function of the system state. The traditional state feedback controller is only related to the system state and is not related to the property of the controller, so that the control signal is greatly changed along with the system state, great difficulty is brought to the execution of the controller, the control signal is passively generated, and the control signal is difficult to generate under the condition that the system state cannot be obtained.
The existing parallel control method for the intelligent workshop is characterized in that a parallel control simulation platform is built, a parallel execution mechanism is built, a parallel control system is corrected and optimized, the intelligent workshop system is controlled in parallel, and stable control signals are generated by combining the state and the control state of the workshop system, so that the real-time monitoring, the three-dimensional visual display and the real-time regulation and control of the workshop running state are realized. However, the above method is directed to a complete and accurate linear system model, and cannot be directly applied to a system model with an unknown system part, and has a great limitation in practical application.
Disclosure of Invention
The invention aims to overcome the defect that the existing parallel control method cannot be directly applied to a system with an unknown system model part and has larger application limitation.
In order to solve the technical problems, the technical scheme of the invention is as follows:
in a first aspect, the present invention provides a parallel control method for system model part unknown, which includes the following steps:
s1: constructing an RBF neural network, approximating an unknown part of a system model by using the RBF neural network, and reconstructing the system model to obtain a reconstructed system model;
s2: constructing a sliding mode function according to the reconstruction system model;
s3: and constructing a parallel controller based on the RBF neural network and the sliding mode function, and controlling the system to run to a balanced state by using the parallel controller.
As a preferred scheme, in S1, for an unknown part of the system model, constructing an RBF neural network specifically includes: and aiming at the unknown part of the system model, determining the number of nodes of an input layer, a hidden layer and an output layer of the RBF neural network, selecting a Gaussian function as an activation function, and taking a weight matrix between the input layer and the hidden layer as a unit matrix to obtain the RBF neural network.
Preferably, the unknown part of the system model comprises a continuous time state function.
As a preferred scheme, in S1, the system model is reconstructed by using the unknown continuous time state function of the RBF neural network approximation system model to obtain a reconstructed system model
Figure BDA0003604456490000021
The expression is as follows:
Figure BDA0003604456490000022
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003604456490000023
representing an unknown continuous time state function approximated by the RBF neural network for the output of the RBF neural network;
Figure BDA0003604456490000024
representing the input of the RBF neural network, and being an n-dimensional system state vector;
Figure BDA0003604456490000025
represents an estimate of an ideal weight matrix between a hidden layer and an output layer in the RBF neural network, T represents a transpose of the matrix, h (x) represents an output of a gaussian basis function of the RBF neural network,
Figure BDA0003604456490000026
is an n-dimensional system control vector.
Preferably, in S2, a sliding mode function S is constructed according to the reconstructed system model, and its expression is as follows:
Figure BDA0003604456490000027
wherein c is an adjustable parameter and meets the Hurwitz condition.
Preferably, in S3, the parallel controller includes a switching component and a continuous component; the switching component control system moves towards the sliding mode surface rapidly, the continuous component control system moves along the sliding mode surface until the system runs to the balance state, and the expression is as follows:
Figure BDA0003604456490000028
Figure BDA0003604456490000029
Figure BDA00036044564900000210
wherein k >0, and
Figure BDA00036044564900000211
wherein the content of the first and second substances,
Figure BDA0003604456490000031
is a parallel controller, u is a control signal,
Figure BDA0003604456490000032
representing the continuous component of the parallel controller,
Figure BDA0003604456490000033
the switching component of the parallel controller is such that,
Figure BDA0003604456490000034
is composed of
Figure BDA0003604456490000035
Derivative of e bound Represents the upper bound of the approximation error of the RBF neural network, sgn (·) represents a symbolic function, and k is an adjustable parameter greater than zero.
As an optimal scheme, after a sliding mode function of a reconstruction system model is obtained, an updating law of an estimated value of an ideal weight matrix between a hidden layer and an output layer in the RBF neural network is designed
Figure BDA0003604456490000036
Using the update law
Figure BDA0003604456490000037
Updating an estimate of an ideal weight matrix
Figure BDA0003604456490000038
The update law
Figure BDA0003604456490000039
The expression of (a) is as follows:
Figure BDA00036044564900000310
where γ is the settable learning rate.
In a second aspect, the present invention further provides a system model part unknown-oriented parallel control system, which is applied to the system model part unknown-oriented parallel control method according to any of the above schemes, and includes:
the RBF neural network building module is used for building an RBF neural network;
the system reconstruction module is used for reconstructing the system model by utilizing the unknown part of the RBF neural network approximation system model to obtain a reconstructed system model;
the sliding mode function design module is used for constructing a sliding mode function of the reconstruction system model;
the parallel controller building module is used for building a parallel controller based on the RBF neural network and the sliding mode function;
and the control module is used for controlling the system to run to a balance state by utilizing the parallel controller.
Preferably, the unknown part of the system model is a continuous time state function.
In a third aspect, the present invention further provides a computer system, which includes a memory and a processor, where the memory stores a computer program, and the processor implements the steps of any of the above parallel control methods facing the system model part unknown when executing the computer program in the memory.
Compared with the prior art, the technical scheme of the invention has the beneficial effects that: the invention utilizes the RBF neural network to approach the unknown part of the system model to obtain a complete reconstructed system model, designs the corresponding parallel controller to control the system, and leads the system to run to a balanced state, thus leading the closed-loop system to tend to be stable, effectively solving the problem that the control signal is difficult to generate when the system state can not be obtained under the condition that the system model is partially unknown, and being capable of being widely applied to the actual system with the partially unknown system model.
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FIG. 1 is a flow chart of a parallel control method oriented to a system model part unknown.
FIG. 2 is a schematic diagram of a system model-oriented partially unknown parallel control method.
Fig. 3 is a schematic diagram of a parallel controller.
FIG. 4 is an architecture diagram of a parallel control system partially unknown to the system model.
Detailed Description
The drawings are for illustrative purposes only and are not to be construed as limiting the patent;
the technical solution of the present invention is further described below with reference to the accompanying drawings and examples.
Example 1
The embodiment provides a parallel control method facing system model part unknown, referring to fig. 1, where fig. 1 is a flowchart of the parallel control method facing system model part unknown, including the following steps:
s1: and constructing an RBF neural network, approximating an unknown part of a system model by using the RBF neural network, and reconstructing the system model to obtain a reconstructed system model.
S2: and constructing a sliding mode function of the reconstruction system model.
S3: and constructing a parallel controller based on the RBF neural network and the sliding mode function, and controlling the system to run to a balanced state by using the parallel controller. The equilibrium state refers to a system state x where the derivative is equal to 0, i.e. the system is not changed after running to this state and is stable.
Because the system model is partially unknown, in order to obtain better performance, the RBF neural network is required to approximate the unknown part of the system model in the design process of the parallel controller, and the system model is reconstructed. The RBF (Radial Basis Function) neural network has a universal approximation characteristic, and can approximate any nonlinear Function under a compact set and any precision. The invention combines the input and output data of the existing system with the RBF neural network, and continuously corrects the weight of the RBF neural network to fit the functional relation between the input variable and the output variable, so that the error between the predicted output and the actual output is minimum, and the self-adaptive approximation of the unknown part of the system model is realized.
In addition, the conventional state feedback controller u is-Kx, and the control signal is directly obtained from the state of the system, but when the state of the system is difficult to obtain or cannot be obtained, the control signal cannot be obtained. Therefore, the invention provides a parallel control method, a corresponding parallel controller is designed, and the change of the control signal of the system is not only related to the system state, but also related to the parallel controller.
The invention obtains a complete reconstruction system model by utilizing the unknown part of the RBF neural network approximation system model, designs a corresponding parallel controller to control the system, effectively solves the problem that a control signal is difficult to generate when the system state cannot be obtained under the condition that the system model is partially unknown, and can be widely applied to system models with unknown system parts such as a motor control system, a robot control system, a servo system, an aircraft motion control system and the like.
Example 2
Referring to fig. 2, fig. 2 is a schematic diagram of a parallel control method facing system model part unknown, and the embodiment provides a parallel control method facing system model part unknown, which includes the following steps:
s1: and constructing an RBF neural network, approximating an unknown part of a system model by using the RBF neural network, and reconstructing the system model to obtain a reconstructed system model.
In this embodiment, the expression of the system model is as follows:
Figure BDA0003604456490000051
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003604456490000052
is a system state vector of dimension n,
Figure BDA0003604456490000053
is a system control vector of dimension n,
Figure BDA0003604456490000054
for the unknown part of the system, f (x) of this embodiment is an unknown continuous time state function, and f (0) ═ 0, f (x) is Lipschitz continuous.
In this embodiment, the number of nodes of the input layer, the hidden layer, and the output layer is determined for an unknown part of the system model, and a gaussian function is selected as an activation function. In order to accelerate the training speed of the neural network, the weight matrix of the input layer and the hidden layer is used as a unit matrix, the weight is not updated, and the expression of the initial RBF neural network is as follows:
f(x)＝W *T h(x)+ε
wherein x represents the input to the RBF neural network; w * And representing an ideal weight matrix between a hidden layer and an output layer in the RBF neural network, wherein epsilon is an approximation error of the RBF neural network. Under a fixed neural network, i.e. under ideal weights, the approximation error of the neural network is bounded, i.e. | ε | ≦ ε bound 。h(x)＝[h j ] T Is output of Gaussian base function of RBF neural network, j represents j node of hidden layer of RBF neural network, h j The expression of (a) is as follows:
Figure BDA0003604456490000055
wherein exp (. cndot.) represents an exponential function based on a natural constant e, c j A central vector representing the jth node of the network, b j Represents the base width parameter of the jth node and is a number greater than zero.
Since the ideal weight of the RBF neural network is unknown, the output of the RBF neural network is adjusted
Figure BDA0003604456490000056
Expressed as:
Figure BDA0003604456490000057
Figure BDA0003604456490000058
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003604456490000059
represents an estimate of an ideal weight matrix between the hidden layer and the output layer in the RBF neural network,
Figure BDA00036044564900000510
is composed of
Figure BDA00036044564900000511
The derivative of (a) of (b),
Figure BDA00036044564900000512
is an estimate of an ideal weight matrix
Figure BDA00036044564900000513
The update law of (2), i.e. the adaptive law of the system model,
Figure BDA00036044564900000514
is the derivative of h (x);
therefore, the system model is reconstructed by using the unknown continuous time state function of the RBF neural network approximation system model to obtain a reconstructed system model
Figure BDA0003604456490000061
The expression is as follows:
Figure BDA0003604456490000062
wherein the content of the first and second substances,
Figure BDA0003604456490000063
representing an unknown continuous time state function approximated by the RBF neural network for the output of the RBF neural network;
Figure BDA0003604456490000064
representing the input of the RBF neural network, and being an n-dimensional system state vector;
Figure BDA0003604456490000065
represents an estimate of an ideal weight matrix between a hidden layer and an output layer in the RBF neural network, T represents a transpose of the matrix, h (x) represents an output of a gaussian basis function of the RBF neural network,
Figure BDA0003604456490000066
is an n-dimensional system control vector.
The invention combines the input and output data of the existing system with the RBF neural network, and continuously corrects the weight of the RBF neural network to fit the functional relation between the input variable and the output variable, so that the error between the predicted output and the actual output is minimum, and the self-adaptive approximation of the unknown part of the system model is realized.
Definition of
Figure BDA0003604456490000067
And if the weight estimation error of the RBF neural network is obtained, then:
Figure BDA0003604456490000068
in this embodiment, the final step of reconstructing the system model using the RBF neural network is used to design an appropriate estimation value of the ideal weight matrix
Figure BDA0003604456490000069
Law of update of
Figure BDA00036044564900000610
The expression is as follows:
Figure BDA00036044564900000611
wherein gamma is a settable learning rate, c is an adjustable parameter, which needs to satisfy the Hurwitz (Helverz) condition, and s is a sliding mode function of the reconstruction system model.
S2: and constructing a sliding mode function according to the reconstruction system model. Sliding mode control is essentially a control strategy for a variable structure control system, and the control characteristic forces the system to move up and down along a specified state track (i.e. a sliding mode surface) with small amplitude and high frequency under certain characteristics, namely, the so-called sliding mode or 'sliding mode' movement. This sliding mode is programmable and independent of system parameters and disturbances. The invention thus designs a parallel controller by means of a sliding mode function.
Design parallelismThe purpose of the controller is to stabilize the system model, i.e. x → 0,
Figure BDA00036044564900000612
the sliding mode function s thus constructed contains x and
Figure BDA00036044564900000613
in normal operation, the sliding mode function is generally defined as:
Figure BDA00036044564900000614
however, since the system model is partially unknown, i.e. f (x) is unknown, the final sliding-mode function s is designed by using the reconstructed system model, and the expression thereof is as follows:
Figure BDA00036044564900000615
the derivative of the sliding-mode function is:
Figure BDA00036044564900000616
i.e. the original system model is expressed as
Figure BDA0003604456490000071
S3: a parallel controller is constructed based on an RBF neural network and a sliding mode function, the system is controlled to run to a balanced state by the parallel controller, namely the derivative of the system state x is equal to 0, and the system does not change after running to the state, so that stability is achieved.
In this embodiment, the parallel controller includes a switching component and a continuous component; the switching component control system moves fast to the sliding mode surface, and the continuous component control system moves along the sliding mode surface until the system runs to the equilibrium state, as shown in fig. 3, and fig. 3 is a schematic diagram of a parallel controller, and the expression of the schematic diagram is as follows:
Figure BDA0003604456490000072
Figure BDA0003604456490000073
Figure BDA0003604456490000074
wherein k >0, and
Figure BDA0003604456490000075
Figure BDA0003604456490000076
wherein the content of the first and second substances,
Figure BDA0003604456490000077
is a parallel controller, u is a control signal,
Figure BDA0003604456490000078
representing the continuous component of the parallel controller,
Figure BDA0003604456490000079
the switching component of the parallel controller is such that,
Figure BDA00036044564900000710
is composed of
Figure BDA00036044564900000711
Derivative of e bound Represents the upper bound of the approximation error of the RBF neural network, sgn (·) represents a symbolic function, and k represents an adjustable parameter greater than zero.
The parallel controller is based on the system unknown part and adaptive law approximated by the RFF neural network
Figure BDA00036044564900000712
And generating a control signal, and inputting the control signal into an actual system, thereby achieving the effect of stabilizing the control system.
Example 3
This embodiment provides a system model part-unknown-oriented parallel control system, as shown in fig. 4, where fig. 4 is an architecture diagram of the system model part-unknown-oriented parallel control system, and the architecture diagram includes: the system comprises an RBF neural network construction module, a system reconstruction module, a sliding mode function design module, a parallel controller construction module and a control module.
In a specific implementation process, the RBF neural network building module determines the number of nodes of an input layer, a hidden layer and an output layer aiming at an unknown part of a system model, selects a Gaussian function as an activation function, and makes a weight matrix between the input layer and the hidden layer as a unit matrix so as to build the RBF neural network.
The system reconstruction module reconstructs the system model by approximating the unknown part of the system model by using the RBF neural network, continuously corrects the weight of the RBF neural network by combining the input and output data of the existing system with the RBF neural network to fit the functional relation between the input variable and the output variable, so that the error between the predicted output and the actual output is minimum, the self-adaptive approximation of the unknown part of the system model is realized, and the reconstructed system model is obtained.
And constructing a sliding mode function of the reconstruction system model by a sliding mode function design module.
And the parallel controller building module builds a parallel controller based on the RBF neural network and the sliding mode function.
And the control module controls the system to run to an equilibrium state by using the parallel controller. Wherein the parallel controller comprises a switching component and a continuous component; the switching component control system moves towards the sliding mode surface rapidly, and the continuous component control system moves along the sliding mode surface until the system runs to a balance state, so that the closed-loop system tends to be stable.
The terms describing positional relationships in the drawings are for illustrative purposes only and are not to be construed as limiting the patent;
it should be understood that the above-described embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the embodiments of the present invention. Other variations and modifications will be apparent to persons skilled in the art in light of the above description. And are neither required nor exhaustive of all embodiments. Any modification, equivalent replacement, and improvement made within the spirit and principle of the present invention should be included in the protection scope of the claims of the present invention.

Claims (10)

1. A parallel control method facing system model partial unknown comprises the following steps:
s1: constructing an RBF neural network, approximating an unknown part of a system model by using the RBF neural network, and reconstructing the system model to obtain a reconstructed system model;
s2: constructing a sliding mode function according to the reconstruction system model;
s3: and constructing a parallel controller based on the RBF neural network and the sliding mode function, and controlling the system to run to a balanced state by using the parallel controller.
2. The system model partially unknown parallel control method according to claim 1, wherein in S1, the construction of the RBF neural network according to the unknown portion of the system model specifically includes:
and aiming at the unknown part of the system model, determining the number of nodes of an input layer, a hidden layer and an output layer of the RBF neural network, selecting a Gaussian function as an activation function, and taking a weight matrix between the input layer and the hidden layer as a unit matrix to obtain the RBF neural network.
3. The system model partially unknown parallel control method as claimed in claim 1, characterized in that the unknown part of the system model comprises a continuous time state function.
4. The parallel control method for system model partial unknowns as claimed in claim 3, wherein in S1, the RBF neural network is used to approximate the unknown continuous time state function of the system model, and the system model is reconstructed to obtain a reconstructed system model
Figure FDA0003604456480000011
The expression is as follows:
Figure FDA0003604456480000012
wherein the content of the first and second substances,
Figure FDA0003604456480000013
representing an unknown continuous time state function approximated by the RBF neural network for the output of the RBF neural network;
Figure FDA0003604456480000014
representing the input of the RBF neural network, and being an n-dimensional system state vector;
Figure FDA0003604456480000015
represents an estimate of an ideal weight matrix between a hidden layer and an output layer in the RBF neural network, T represents a transpose of the matrix, h (x) represents an output of a gaussian basis function of the RBF neural network,
Figure FDA0003604456480000016
is an n-dimensional system control vector.
5. The system model partially unknown parallel control method according to claim 4, wherein in S2, according to the reconstructed system model, a sliding mode function S is constructed, whose expression is as follows:
Figure FDA0003604456480000017
wherein c is an adjustable parameter and meets the Hurwitz condition.
6. The system model partially unknown parallel control method according to claim 5, characterized in that in S3, said parallel controller comprises a switching component and a continuous component; the switching component control system moves towards the sliding mode surface rapidly, the continuous component control system moves along the sliding mode surface until the system runs to the balance state, and the expression is as follows:
Figure FDA0003604456480000021
Figure FDA0003604456480000022
Figure FDA0003604456480000023
wherein k >0, and
Figure FDA0003604456480000024
wherein the content of the first and second substances,
Figure FDA0003604456480000025
is a parallel controller, u is a control signal,
Figure FDA0003604456480000026
representing the continuous component of the parallel controller,
Figure FDA0003604456480000027
the switching component of the parallel controller is such that,
Figure FDA0003604456480000028
is composed of
Figure FDA0003604456480000029
Derivative of e bound Represents the upper bound of the approximation error of the RBF neural network, sgn (·) represents a symbolic function, and k is an adjustable parameter greater than zero.
7. The parallel control method for system model part unknowns according to claim 5, further comprising designing an update law of an estimated value of an ideal weight matrix between a hidden layer and an output layer in the RBF neural network after obtaining a sliding mode function for reconstructing the system model
Figure FDA00036044564800000211
Using the update law
Figure FDA00036044564800000214
Updating an estimate of an ideal weight matrix
Figure FDA00036044564800000213
The update law
Figure FDA00036044564800000212
The expression of (c) is as follows:
Figure FDA00036044564800000210
where γ is the settable learning rate.
8. A system model partially unknown-oriented parallel control system applied to the system model partially unknown-oriented parallel control method according to any one of claims 1 to 7, comprising:
the RBF neural network building module is used for building an RBF neural network;
the system reconstruction module is used for reconstructing the system model by utilizing the unknown part of the RBF neural network approximation system model to obtain a reconstructed system model;
the sliding mode function design module is used for constructing a sliding mode function of the reconstruction system model;
the parallel controller building module is used for building a parallel controller based on the RBF neural network and the sliding mode function;
and the control module is used for controlling the system to run to a balance state by utilizing the parallel controller.
9. The system-model-partially-unknown-oriented parallel control system according to claim 8, wherein the unknown portion of the system model is a continuous time-state function.
10. A computer system comprising a memory having a computer program stored thereon and a processor that when executing the computer program in the memory performs the steps of the system model part agnostic parallelism control method according to any one of claims 1 to 7.
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Publication number Priority date Publication date Assignee Title
CN116909136A (en) * 2023-06-21 2023-10-20 山东大学 2-DOF helicopter sliding mode control method and system based on determined learning

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116909136A (en) * 2023-06-21 2023-10-20 山东大学 2-DOF helicopter sliding mode control method and system based on determined learning
CN116909136B (en) * 2023-06-21 2023-12-26 山东大学 2-DOF helicopter sliding mode control method and system based on determined learning

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