CN110888323A - Control method for intelligent optimization of switching system - Google Patents

Control method for intelligent optimization of switching system Download PDF

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CN110888323A
CN110888323A CN201911173592.6A CN201911173592A CN110888323A CN 110888323 A CN110888323 A CN 110888323A CN 201911173592 A CN201911173592 A CN 201911173592A CN 110888323 A CN110888323 A CN 110888323A
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subsystem
cost function
network
weight
switching
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赵旭东
王佩蓉
沈亮
张硕
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Dalian University of Technology
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
    • G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G05B13/0265—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric the criterion being a learning criterion
    • G05B13/027—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric the criterion being a learning criterion using neural networks only

Abstract

The invention discloses a control method for intelligent optimization of a switching system, and belongs to the technical field of optimization control of switching systems. Compared with the prior art, the method provided by the invention can combine the traditional advanced methods of optimal control and artificial intelligence, and further provides an optimal control scheme for a plurality of complex nonlinear systems. The invention adopts a neural network method, designs an optimization control method for a switching system in MATLAB software according to the basic principle of self-adaptive dynamic programming, and simulates. Meanwhile, the problem of controller saturation is considered in the method design, and simulation that some switching systems are more consistent with actual conditions is achieved. The method has the advantages of fast operation, simple operation and the like, can realize the stability of the controller in the whole switching process, has good expansibility, can be used in a system with more complexity and more state dimensions, and can be applied to wider practical fields.

Description

Control method for intelligent optimization of switching system
Technical Field
The invention belongs to the technical field of optimization control of a switching system, and particularly relates to a control method for intelligent optimization of the switching system.
Background
The switching system is a close description of the actual system and also of the complexity of the study, it is composed of a set of subsystems with different dynamics, each of which is active at every moment. Therefore, in order to control such a system, a set of explicit switching time sequences and control (input) quantities need to be calculated. As switching systems have gained applications in computer science, mathematics, aerospace and chemical engineering, there has been a growing interest in the research of switching systems. At the earliest, the switching system is mainly studied in two aspects, namely, the stability and the synchronism of the switching system and the optimal control problem of the switching system, and the basic purpose of the method is to design a controller on the premise of meeting certain switching performance indexes. The current research on the optimal control of switching systems is mainly divided into two categories: the first type is a switching sequence of subsystems, i.e. a mode sequence, which is selected by experience of the predecessor, so that only the switching instant between modes needs to be determined. The second category is to handle a limited number of subsystems based on discretized problem space. A general use of direct search evaluates the cost function of different randomly selected switching time sequences in a limited number of options to select the best sequence. In conclusion, the optimization control research of the switching system has important guiding significance for a series of industrial engineering technical problems such as automatic scheduling, production process automation, robot control and computer communication. It is necessary to study the optimal control of the handover system.
In the prior art, many algorithm designs of intelligent optimization control are designed only by using a minimized idea, and the problems of low optimization efficiency and low optimization precision exist.
Disclosure of Invention
The invention provides a control method for intelligent optimization of a switching system based on self-adaptive dynamic programming, which aims to solve the problems of low optimization efficiency and low optimization precision in the prior art. Compared with the prior art, the method provided by the invention can combine the traditional advanced methods of optimal control and artificial intelligence, and further provides an optimal control scheme for a plurality of complex nonlinear systems. The invention adopts a neural network method, designs an optimization control method for a switching system in MATLAB software according to the basic principle of self-adaptive dynamic programming, and simulates. Meanwhile, the problem of controller saturation is considered in the method design, and simulation that some switching systems are more consistent with actual conditions is achieved.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
a control method for intelligent optimization of a switching system takes controller saturation as a constraint condition and takes switching sequences of direction control variables and subsystems as optimization parameters, and comprises the following steps:
step 1, establishing a switching system model
Because the switching system comprises a plurality of subsystems, and the controller has a control function on each subsystem, the switching system model is established as follows:
Figure BDA0002289386460000021
wherein
Figure BDA0002289386460000022
Is a state function differential form of the system, faAnd gaIs a system parameter of subsystem a and a ∈ Ω ≡ {1, 2. }, u (t) e RmIs a directional control variable of the system, x (t) e RnIs a position state variable;
step 2, calculating an optimal cost function
In order to study the state in the optimization process more clearly, discretization processing is carried out on the formula (1), and a discretized switching system model is as follows:
xk+1＝fak(xk)+gak(xk)uk(2)
wherein xkIs the position state of the k-th discretization, xk+1Is the position state of the k +1 th step of discretization, ukIs a discretized direction control variable, fakAnd gakIs the discretized subsystem parameter of the subsystem aCounting;
according to the optimization target, the optimization problem of the switching system needs to establish a cost function which is related to the system and is definite to be optimized, and a discretized cost function J of the k stepk(xk) Is composed of
Jk(xk)＝Q+uk TNuk+Jk+1(xk+1) (3)
Wherein the state weight Q and the control weight N are semi-positive definite matrices, Jk+1(xk+1) The cost function of the next step k +1 is adopted, and the required target is finally achieved on the basis of meeting the stability of the whole system in the whole optimization process;
according to the discretized cost function, the optimal direction control variable u of the corresponding subsystem is obtained by taking the minimum subsystem cost function as a targetk a,*：
Figure BDA0002289386460000031
Further, the variable u is controlled in the optimum directionk a,*Under the action of (3), obtaining an optimal cost function Jk *(xk)：
Jk *(xk)＝Q+mina∈Ω(uk a,*TNuk a,*+Jk+1 *(fak(xk)+gak(xk)uk a,*)) (5)
Step 3,
When the adaptive dynamic programming method and the neural network are used for designing the controller meeting the optimized control target of the switching system, the adaptive dynamic programming method comprises an evaluation network and an execution network, so that the position state variable value is randomly selected as a training sample at first, and the weight of the initial execution network is obtained
Figure BDA0002289386460000033
And the weight W of the initial evaluation networkN；
Step 4, calculating the weight of the execution network
Figure BDA0002289386460000032
Setting the number p of hidden layer neurons in the execution network by using a neural network method, and enabling the number of input layer neurons to be the same as that of position state variables and enabling the number of output layer neurons to be the same as that of direction control variables; meanwhile, the number q of hidden layer neurons is set in the evaluation network, the input layer neurons are determined by the number of position state variables, and the output layer neurons are related to the number of costs;
the optimal direction control variable uk a,*And an optimal cost function Jk *Are respectively approximated as:
Figure BDA0002289386460000041
Figure BDA0002289386460000042
wherein σ is Rn→Rp，φ:Rn→RqIt is a basic function, which is composed of a non-repeated polynomial with the system state as a parameter;
calculating the execution network weight value by the formulas (4) and (6)
Figure BDA0002289386460000043
The following were used:
Figure BDA0002289386460000044
step 5, updating the weight of the execution network
Figure BDA0002289386460000045
Establishing an updating iterative formula:
Figure BDA0002289386460000046
wherein i is the number of iterations;
because the initial state of the system is changed frequently in the actual process, in order to make the program run quickly in different initial states and make the training part as much as possible and sufficient, the training and the on-line running need to be carried out separately; and aiming at the problem of controller saturation, adding the limit of threshold value on the size of the direction control variable in the solving process of the formula (9);
the change in the direction control variable is first limited to the range of:
Figure BDA0002289386460000047
wherein D is a hyperbolic tangent function, U is a threshold value of the control signal, and v represents a multiplied variable in the integral;
controlling weights of execution network
Figure BDA0002289386460000048
The recursive iterative relationship of (a) is performed according to the following equation:
Figure BDA0002289386460000049
step 6, calculating a cost function of each subsystem
Calculating the cost function of each subsystem through a formula (3), comparing the cost functions of different subsystems and selecting the minimum cost function;
step 7, calculating and evaluating network weight
According to the least square principle, combining the weight of the execution network, and adopting the following formula to calculate and evaluate the network weight Wk：
Figure BDA0002289386460000051
Step 8, outputting the optimal direction control variable and the switching sequence of the subsystem
And calculating the optimal direction control variable and a cost function under the operation of each subsystem by using the execution network weight and the evaluation network weight after considering the constraint condition, gradually selecting the subsystem corresponding to the minimum cost function as a selection condition, and finally obtaining the switching sequence of the subsystem.
The invention has the beneficial effects that:
the optimization of many existing switching systems depends on a system model for optimization, and a global optimization control method which does not depend on the system model is difficult to obtain. The invention provides an optimal control method of a switching system without depending on an initial state and under the condition of controller saturation based on a self-adaptive dynamic programming method and a neural network aiming at the design of the method for performing optimal control on the switching system, the operation is fast, the operation is simple, the stability of the controller in the whole switching process can be realized, the method has good expansibility, can be used in a more complex system with more state dimensions, and can be applied to a wider practical field.
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FIG. 1 is a flow chart of an optimization control algorithm process for a switching system;
FIG. 2 is a block diagram of a switching system;
FIG. 3 is a graph of control quantities of a hybrid vehicle under controller saturation constraints;
FIG. 4 is a graph of a switching sequence of a hybrid vehicle under controller saturation constraints.
Detailed Description
In order to make the objects, features and advantages of the present invention more obvious and understandable, the present invention is further described below with reference to the accompanying drawings in combination with the embodiments so that those skilled in the art can implement the present invention by referring to the description, and the scope of the present invention is not limited to the embodiments. It is to be understood that the embodiments described below are only some embodiments of the present invention, and not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The following is a specific description of the implementation and operation process of the switching system of two modes, including two modes of the hybrid electric vehicle, where the mode 1 is a gasoline driving mode, and the mode 2 is an electric driving mode, as shown in fig. 2. The two systems are independent from each other, on the premise of sufficient energy, the direction and position are continuous control signals, the minimum cost function is taken as a target, and on the premise of uncertain switching sequences, the optimization control steps are as follows (the optimization control flow is shown in fig. 1):
step 1, establishing a switching system model
Because the switching system comprises a plurality of subsystems, each subsystem is analyzed, and the controller of the system has a control function on each subsystem, the switching system model is established as follows:
Figure BDA0002289386460000061
wherein
Figure BDA0002289386460000062
Is a state function differential form of the system, faAnd gaIs a system parameter of subsystem a and a ∈ Ω ≡ {1, 2. }, u (t) e RmIs a directional control variable of the system, x (t) e RnIs a position state variable;
step 2, calculating an optimal cost function
In order to study the state in the optimization process more clearly, discretization processing is carried out on the formula (1), and a discretized switching system model is as follows:
xk+1＝fak(xk)+gak(xk)uk(2)
wherein xkIs the position state of the k-th discretization, xk+1Is the position state of the k +1 th step of discretization, ukIs a discretized direction control variable, fakAnd gakIs the subsystem parameter after the discretization of the subsystem a;
based on the optimization objective, switching systemsThe optimization problem of the system needs to establish a cost function related to the system and definite variables to be optimized, and the discretized cost function J of the k stepk(xk) Is composed of
Jk(xk)＝Q+uk TNuk+Jk+1(xk+1) (3)
Wherein the state weight Q and the control weight N are semi-positive definite matrices, Jk+1(xk+1) The cost function of the next step k +1 is adopted, and the required target is finally achieved on the basis of meeting the stability of the whole system in the whole optimization process;
according to the discretized cost function, the optimal direction control variable u of the corresponding subsystem is obtained by taking the minimum subsystem cost function as a targetk a,*：
Figure BDA0002289386460000074
Further, the variable u is controlled in the optimum directionk a,*Under the action of (3), obtaining an optimal cost function Jk *(xk)：
Jk *(xk)＝Q+mina∈Ω(uk a,*TNuk a,*+Jk+1 *(fak(xk)+gak(xk)uk a,*)) (5)
Step 3, randomly selecting the position state variable value as a training sample, and randomly selecting 200 state values for training as the state number in the system is 2; and thus obtain the weight of the initial execution network
Figure BDA0002289386460000071
And the weight W of the initial evaluation networkN；
Step 4, calculating the weight of the execution network
Figure BDA0002289386460000072
Calculate each childThe execution network weight of the system uses a neural network method to make the number of hidden layer neurons in the execution network p, at this time, p is selected to be 10, the input layer neuron is 1, and the output layer neuron is also 1. Similarly, when the number of hidden layer neurons in the evaluation network is q, and q is 18, the number of input layer neurons is 1, and the number of output layer neurons is also 1, the optimal direction control variable u is the optimal direction control variable qk a,*And an optimal evaluation function Jk *Are respectively approximated as:
Figure BDA0002289386460000073
Figure BDA0002289386460000081
wherein σ is Rn→Rp，φ:Rn→RqIt is a basic function, which is composed of a non-repeated polynomial with the system state as a parameter;
calculating the execution network weight value by the formulas (4) and (6)
Figure BDA0002289386460000082
The following were used:
Figure BDA0002289386460000083
step 5, updating the weight of the execution network
Figure BDA0002289386460000084
Establishing an updating iterative formula:
Figure BDA0002289386460000085
wherein i is the number of iterations;
because the initial state of the system is changed frequently in the actual process, in order to make the program run quickly in different initial states and make the training part as much as possible and sufficient, the training and the on-line running need to be carried out separately; and aiming at the problem of controller saturation, adding the limit of threshold value on the size of the direction control variable in the solving process of the formula (9);
the change in the direction control variable is first limited to the range of:
Figure BDA0002289386460000086
wherein D is a hyperbolic tangent function, U is a threshold value of the control signal, and v represents a multiplied variable in the integral;
controlling weights of execution network
Figure BDA0002289386460000087
The recursive iterative relationship of (a) is performed according to the following equation:
Figure BDA0002289386460000088
step 6, calculating a cost function of each subsystem
Calculating the cost function of each subsystem through a formula (3), comparing the cost functions of different subsystems and selecting the minimum cost function;
step 7, calculating and evaluating network weight
According to the least square principle, combining the weight of the execution network, and adopting the following formula to calculate and evaluate the network weight Wk：
Figure BDA0002289386460000091
Step 8, outputting the optimal direction control variable and the switching sequence of the subsystem
Performing online operation, performing online operation by using the network weight and the evaluation network weight after considering the constraint condition, and performing optimization control on the model of the switching system to obtain the size of a controlled variable, as shown in fig. 3, and the switching sequence of the subsystem, as shown in fig. 4;
the above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art should be considered to be within the technical scope of the present invention, and the technical solutions and the inventive concepts thereof according to the present invention should be equivalent or changed within the scope of the present invention.

Claims (1)

1. A control method for intelligent optimization of a switching system takes controller saturation as a constraint condition and takes a switching sequence of direction control variables and subsystems as an optimization parameter, and is characterized by comprising the following steps of:
step 1, establishing a switching system model
Because the switching system comprises a plurality of subsystems, and the controller has a control function on each subsystem, the switching system model is established as follows:
Figure FDA0002289386450000011
wherein
Figure FDA0002289386450000012
Is a state function differential form of the system, faAnd gaIs a system parameter of subsystem a and a ∈ Ω ≡ {1, 2. }, u (t) e RmIs a directional control variable of the system, x (t) e RnIs a position state variable;
step 2, calculating an optimal cost function
In order to study the state in the optimization process more clearly, discretization processing is carried out on the formula (1), and a discretized switching system model is as follows:
xk+1＝fak(xk)+gak(xk)uk(2)
wherein xkIs the position state of the k-th discretization, xk+1Is the position state of the k +1 th step of discretization, ukIs a discretized direction control variable, fakAnd gakIs the subsystem parameter after the discretization of the subsystem a;
according toOptimizing the target, and switching the optimization problem of the system requires establishing a cost function of the definite optimized variable related to the system, and discretizing the cost function J of the k stepk(xk) Is composed of
Jk(xk)＝Q+uk TNuk+Jk+1(xk+1)(3)
Wherein the state weight Q and the control weight N are semi-positive definite matrices, Jk+1(xk+1) The cost function of the next step k +1 is adopted, and the required target is finally achieved on the basis of meeting the stability of the whole system in the whole optimization process;
according to the discretized cost function, the optimal direction control variable u of the corresponding subsystem is obtained by taking the minimum subsystem cost function as a targetk a,*：
Figure FDA0002289386450000021
Further, the variable u is controlled in the optimum directionk a,*Under the action of (3), obtaining an optimal cost function Jk *(xk)：
Jk *(xk)＝Q+mina∈Ω(uk a,*TNuk a,*+Jk+1 *(fak(xk)+gak(xk)uk a,*))(5)
Step 3, when the controller meeting the optimized control target of the switching system is designed by using the self-adaptive dynamic programming method and the neural network, the self-adaptive dynamic programming method comprises the steps of evaluating the network and executing the network, randomly selecting the position state variable value as a training sample, and obtaining the weight of the initial executing network
Figure FDA0002289386450000022
And the weight W of the initial evaluation networkN；
Step 4, calculating the weight of the execution network
Figure FDA0002289386450000023
Setting the number p of hidden layer neurons in the execution network by using a neural network method, and enabling the number of input layer neurons to be the same as that of position state variables and enabling the number of output layer neurons to be the same as that of direction control variables; meanwhile, the number q of hidden layer neurons is set in the evaluation network, the input layer neurons are determined by the number of position state variables, and the output layer neurons are related to the number of costs;
the optimal direction control variable uk a,*And an optimal cost function Jk *Are respectively approximated as:
Figure FDA0002289386450000024
Figure FDA0002289386450000025
wherein σ is Rn→Rp，φ:Rn→RqIt is a basic function, which is composed of a non-repeated polynomial with the system state as a parameter;
calculating the execution network weight value by the formulas (4) and (6)
Figure FDA0002289386450000026
The following were used:
Figure FDA0002289386450000027
step 5, updating the weight of the execution network
Figure FDA0002289386450000028
Establishing an updating iterative formula:
Figure FDA0002289386450000031
wherein i is the number of iterations;
because the initial state of the system is changed frequently in the actual process, in order to make the program run quickly in different initial states and make the training part as much as possible and sufficient, the training and the on-line running need to be carried out separately; and aiming at the problem of controller saturation, adding the limit of threshold value on the size of the direction control variable in the solving process of the formula (9);
the change in the direction control variable is first limited to the range of:
Figure FDA0002289386450000032
wherein D is a hyperbolic tangent function, U is a threshold value of the control signal, and v represents a multiplied variable in the integral;
controlling weights of execution network
Figure FDA0002289386450000033
The recursive iterative relationship of (a) is performed according to the following equation:
Figure FDA0002289386450000034
step 6, calculating a cost function of each subsystem
Calculating the cost function of each subsystem through a formula (3), comparing the cost functions of different subsystems and selecting the minimum cost function;
step 7, calculating and evaluating network weight
According to the least square principle, combining the weight of the execution network, and adopting the following formula to calculate and evaluate the network weight Wk：
Figure FDA0002289386450000035
Step 8, outputting the optimal direction control variable and the switching sequence of the subsystem
And calculating the optimal direction control variable and a cost function under the operation of each subsystem by using the execution network weight and the evaluation network weight after considering the constraint condition, gradually selecting the subsystem corresponding to the minimum cost function as a selection condition, and finally obtaining the switching sequence of the subsystem.
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