An optimal control method and device for synchronous switching of a multi-agent system and a medium

Abstract

The application discloses a kind of optimal control method, device and medium of synchronous switching multi-agent system, including subsystem selection module and optimal control module;Subsystem selection module: the objective function value corresponding to each subsystem is calculated at any time, and the subsystem with minimum objective function value is selected to run;Optimal control module determines optimal control input according to the selected subsystem model, coordination vector and objective function weight matrix.The present application is aimed at a kind of synchronous switching multi-agent system, the switching time of each agent subsystem and the selected subsystem model are all same, provide a kind of globally optimal switching and control strategy, by minimizing the objective function about state and input, the analytical expression of optimal switching function determining subsystem selection and optimal control law regulating subsystem state evolution is given.

Description

Technical Field

[0001] This invention belongs to the interdisciplinary technical field of multi-agent systems, switching systems and optimal control, and particularly relates to an optimal control method, device and medium for synchronously switching multi-agent systems. Background Technology

[0002] Multi-powered vehicle swarms are a typical example of switchable multi-agent systems. For instance, drones can be categorized by energy source: battery-powered, solar-powered, and fuel-powered. Multi-powered drones can utilize photovoltaic cells to reduce the mass of the base battery and leverage the coupling of power sources with different power densities to improve maneuverability, achieving long endurance and energy conservation and emission reduction. For swarm control of multi-powered vehicles, each vehicle needs to employ different combinations of heterogeneous power sources under varying operating conditions to achieve optimal trajectory tracking or formation control performance, enabling rapid maneuverability and high-precision tracking. In a switchable multi-agent system, each agent is a switching system, and multiple switching systems are connected through a specific communication topology to form a multi-agent system.

[0003] Currently, research on multi-agent systems with dynamic switching of communication network topologies is relatively mature in both basic and applied basic research, while research on multi-agent systems with dynamic switching of agent dynamics is relatively lacking. Related research results on switched multi-agent systems mainly focus on output consensus and distributed robust control. The literature (Yilun Shang, Resilient consensus of switched multi-agent systems, Systems & Control Letters, Volume 122, 2018, Pages 12-18.) presents a resilient consensus algorithm with Byzantine nodes; however, its agent evolution model only contains one continuous and one discrete dynamic equation. The literature (Jun Zhao, David J. Hill, Tao Liu, Synchronization of complex dynamical networks with switching topology: Aswitched system point of view, Automatica, Volume 45, Issue 11, 2009, Pages 2502-2511.) studies the consensus criteria and stability conditions of multi-agent systems under arbitrarily switched and finitely switched communication topologies from the perspective of switched systems. The paper (W. Zhang, DWCHo, Y. Tang and Y. Liu, Quasi-Consensus of Heterogeneous-Switched Nonlinear Multiagent Systems, IEEE Transactions on Cybernetics, vol. 50, no. 7, pp. 3136-3146, July 2020.) studies the bounded consistency problem of heterogeneous nonlinear multiagent systems where communication topology switching and agent mode switching are asynchronous. Currently, research results on the optimal control problem of switched multiagent systems and its applications in specific scenarios are very rare.

[0004] The optimal control problem for switching multiple agents is a global optimization problem involving discrete binary switching variables and continuous control variables. Even in the special case where the subsystems of the agents are all linear and the gains of the agent subsystems and the controller switch synchronously, finding the optimal solution is extremely difficult. Only suboptimal solutions that meet the requirements can be obtained through iterative learning algorithms, such as adaptive dynamic programming and deep reinforcement learning methods. Furthermore, finding the closed-form analytical solution for the optimal switching mechanism and control law remains an open problem. Summary of the Invention

[0005] The purpose of this invention is to address the shortcomings of existing technologies by providing an optimal control method, device, and medium for synchronously switching multi-agent systems.

[0006] The objective of this invention is achieved through the following technical solution: an optimal control method for a synchronously switching multi-agent system, wherein each agent is a linearly switching system, each agent contains several subsystems, and at any given time, the agent uses a subsystem model as the evolution model for its state trajectory, and the evolution model switches between multiple subsystems; the optimal control method includes:

[0007] Based on the costate vector, the models of each subsystem, and the weight matrix of the objective function, the optimal objective function is constructed. At any time, the objective function value corresponding to each subsystem is calculated, and the subsystem with the smallest objective function value is taken as the evolution model at the current time.

[0008] The optimal control input is determined based on the selected subsystem model, costate vector, and objective function weight matrix.

[0009] Furthermore, the specific steps of constructing the optimal objective function based on the costate vector, the models of each subsystem, and the objective function weight matrix, calculating the objective function value for each subsystem at any given time, and selecting the subsystem with the smallest objective function value as the evolution model at the current time are as follows:

[0010] Step 1: Initialize the weight matrix G of the objective function ij Q ij R ii and initial state x i (0) Initial value λ of the costate variable i (0), 1≤i≤N, 1≤j≤N; terminal time t f Terminal status x i (t f A constant T is given as the sampling period;

[0011] Step 2: Repeat the following steps t f / T times:

[0012] For the j-th subsystem of the synchronous switching multi-agent system, calculate the objective function value, obtain the subsystem index corresponding to its minimum value, and use it as the subsystem to be selected;

[0013] Calculate the costate vector λ using the selected subsystem model and the objective function weight matrix. i (t) and obtain the optimal control input for each agent in the synchronously switching multi-agent system;

[0014] Calculate the state vector x for the next sampling period i (t);

[0015] Step 3: Correct the initial value λ of the costate vector i (0) Until the boundary conditions are met, determine the operating subsystems of the synchronous switching multi-agent system at each moment.

[0016] Furthermore, the switching time and the selected subsystem model of each agent subsystem in the synchronous switching multi-agent system are the same.

[0017] Furthermore, the evolutionary model of the synchronously switching multi-agent system is as follows:

[0018]

[0019] And satisfy 1≤l≤M, where M is the total number of subsystems;

[0020] Where x i (t), where 1≤i≤N is the n-dimensional state vector of agent i in the synchronous switching multi-agent system, and N is the total number of agents; For x i (t) is the derivative with respect to time; u i (t) represents the m-dimensional control input; A l B is the l-th n×n dimensional system matrix of agent i; l Let σ be the l-th m×m-dimensional input matrix of agent i; l (t) is the l-th switching variable of agent i, and σ l (t)∈{0,1}, the switching variable is used to characterize the subsystem switching behavior of agent i;

[0021] The objective of optimal control is to minimize the historical state xi(t) and the terminal state x. i (t f The deviation between the equilibrium point and the quadratic form of the control cost, in a finite time domain [0, t] f Within this scope, the objective function for optimal control of a synchronously switching multi-agent system is defined as follows:

[0022]

[0023] Where T represents the transpose of the vector, G ii G ij Q ii Q ij R is an n×n positive semi-definite matrix; ii It is an m×m positive definite matrix, 1≤i≤N, 1≤j≤N;

[0024] Solving the optimal control problem of a synchronously switching multi-agent system using the maximum principle yields the costate equations:

[0025]

[0026] Where λ i (t) is an n-dimensional costate vector; and satisfies the boundary conditions:

[0027]

[0028] Furthermore, based on the costate vector, the models of each subsystem, and the weight matrix of the objective function, an optimal objective function is constructed. The objective function value for each subsystem is calculated at any given time. The subsystem with the smallest objective function value is taken as the evolution model for the current time step, including:

[0029]

[0030] σ j* =1,σ l =0 (1≤l≤M,l≠j*);

[0031] in This means finding the value that makes j the independent variable. The value of j when it reaches its minimum value is denoted as j. * , is the index of the selected subsystem; A j B j These are model parameters, and the superscript T indicates the transpose operation.

[0032] Furthermore, based on the selected subsystem model, costate vector, and objective function weight matrix, the optimal control input is determined, and the gain matrix of the local feedback is obtained by solving the costate equation.

[0033]

[0034] Furthermore, in the specific implementation steps,

[0035] Step 2: Calculate the state vector for the next sampling period:

[0036]

[0037]

[0038] Step 3: Order X(t) is an nN×nN positive semi-definite matrix; X(t) = [x1(t), ..., x N (t)] T To synchronously switch the n·N dimensional state vector of the multi-agent system at time t; Λ(t)=[λ1(t),…,λ N (t)] T It is an n·N dimensional vector;

[0039] Finding the terminal costate error Λ(t) f )-GX(tf ) Reaching 0 to 1e- 3 The initial value of the costate variable is Λ(0).

[0040] This invention also provides an optimal control device for a synchronously switching multi-agent system, wherein each agent is a linearly switching system, each agent contains several subsystems, and at any given time, the agent uses a subsystem model as the evolution model for its state trajectory, and the evolution model switches between multiple subsystems; the optimal control device includes:

[0041] The intelligent agent subsystem selection module is used to construct the optimal objective function based on the costate vector, the models of each subsystem, and the objective function weight matrix. It calculates the objective function value for each subsystem at any time and selects the subsystem with the smallest objective function value as the evolution model at the current time.

[0042] The agent's optimal control input module is used to determine the optimal control input based on the selected subsystem model, costate vector, and objective function weight matrix.

[0043] The present invention also provides an optimal control device for a synchronously switching multi-agent system, comprising one or more processors for implementing the above-described optimal control method for a synchronously switching multi-agent system.

[0044] The present invention also provides a computer-readable storage medium having a program stored thereon, which, when executed by a processor, is used to implement the above-described optimal control method for a synchronously switching multi-agent system. Attached Figure Description

[0045] To more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0046] Figure 1 This is a schematic diagram of a synchronous switching multi-agent system structure, where circles represent agents and squares represent subsystems contained within an agent;

[0047] Figure 2 It is a state trajectory diagram of a synchronously switching multi-agent system, where x1(1), x1(2), x2(1), and x2(2) represent the two state trajectories of agents 1 and 2, respectively.

[0048] Figure 3 This is a schematic diagram of the modules of the device of the present invention;

[0049] Figure 4This is a hardware structure diagram provided for an embodiment of the present invention. Detailed Implementation

[0050] The following embodiments are only used to more clearly illustrate the technical solutions of the present invention, and should not be construed as limiting the scope of protection of the present invention. The present invention will now be described in detail with reference to the accompanying drawings. Unless otherwise specified, the features in the following embodiments and implementations can be combined with each other.

[0051] The present invention discloses an optimal control method for a synchronously switching multi-agent system, wherein each agent is a linearly switching system, each agent contains multiple subsystems with different evolutionary models, and at any given time, the agent uses one subsystem model as the evolutionary model for its state trajectory, and the evolutionary models switch between multiple subsystems; the optimal control method includes:

[0052] Based on the costate vector, the models of each subsystem, and the weight matrix of the objective function, the optimal objective function is constructed. At any time, the objective function value of the multi-agent system corresponding to each subsystem is calculated, and the subsystem with the smallest objective function value is taken as the evolution model at the current time.

[0053] The optimal control input is determined based on the selected subsystem model, costate vector, and objective function weight matrix.

[0054] The switching behavior between the various intelligent agent subsystems is synchronous, and the subsystem models of each intelligent agent are the same.

[0055] In one embodiment, an optimal objective function is constructed based on the costate vector, the models of each subsystem, and the objective function weight matrix. The objective function value for each subsystem is calculated at any given time, and the subsystem with the smallest objective function value is taken as the evolution model for the current time step. Specifically:

[0056] Step 1: Initialize the weight matrix G of the objective function ij Q ij , Ri and initial state xi(0), initial values ​​of costate variables λi(0), 1≤i≤N, 1≤j≤N; terminal time t f Terminal status x i (t f A constant T is given as the sampling period;

[0057] Step 2: Repeat the following steps t f / T times:

[0058] For the j-th subsystem of the synchronous switching multi-agent system, calculate the objective function value, obtain the subsystem index corresponding to its minimum value, and use it as the subsystem to be selected;

[0059] Calculate the costate vector λ using the selected subsystem model and the objective function weight matrix. i (t) and obtain the optimal control input for each agent in the synchronously switching multi-agent system;

[0060] Calculate the state vector x for the next sampling period i (t);

[0061] Step 3: Correct the initial value λ of the costate vector i (0) Until the boundary conditions are met, determine the operating subsystems of the synchronous switching multi-agent system at each moment.

[0062] In one embodiment, specifically:

[0063] Step 2: Calculate the state vector for the next sampling period:

[0064]

[0065] Calculate the costate vector for the next sampling period:

[0066]

[0067] Step 3: Order X(t) is an nN×nN positive semi-definite matrix; X(t) = [x1(t), ..., x N (t)] T To synchronously switch the n·N dimensional state vector of the multi-agent system at time t; Λ(t)=[λ1(t),…,λ N (t)] T It is an n·N dimensional vector;

[0068] Finding the terminal costate error Λ(t) f )-GX(t f ) Reaching 0 to e -3 The initial value of the costate variable is Λ(0).

[0069] In one embodiment, for a synchronously switching multi-agent system, where the switching time and selected subsystem models of each agent subsystem are identical, a globally optimal switching and control strategy is provided. By minimizing the objective function with respect to state and input, analytical expressions are given for the optimal objective function determining subsystem selection and the optimal control law regulating the evolution of subsystem states. The evolutionary model of the synchronously switching multi-agent system is defined as follows:

[0070]

[0071] And satisfy 1≤l≤M, where M is the total number of subsystems;

[0072] Where xi (t), where 1≤i≤N is the n-dimensional state vector of agent i in the synchronous switching multi-agent system, and N is the total number of agents; For x i (t) is the derivative with respect to time; u i (t) represents the m-dimensional control input; A l B is the l-th n×n dimensional system matrix of agent i; l Let σ be the l-th m×m-dimensional input matrix of agent i; l (t) is the l-th switching variable of agent i, and σ l (t)∈{0,1}, the switching variable is used to characterize the subsystem switching behavior of agent i;

[0073] The objective of optimal control is to minimize the historical state xi(t) and the terminal state x. i (t f The deviation between the equilibrium point and the quadratic form of the control cost, in a finite time domain [0, t] f Within this scope, the objective function for optimal control of a synchronously switching multi-agent system is defined as follows:

[0074]

[0075] Where T represents the transpose of the vector, G ii G ij Q ii Q ij R is an n×n positive semi-definite matrix; ii Let be an m×m positive definite matrix, 1≤i≤N, 1≤j≤N.

[0076] Solving the optimal control problem of a synchronously switching multi-agent system using the maximum principle yields the costate equations:

[0077]

[0078] Where λ i (t) is an n-dimensional costate vector; and satisfies the boundary conditions:

[0079]

[0080] In one embodiment, an optimal objective function is constructed based on the costate vector, the models of each subsystem, and the objective function weight matrix. The objective function value for each subsystem is calculated at any given time, and the subsystem with the smallest objective function value is taken as the evolution model at the current time. This includes:

[0081]

[0082] σ δ(t) =1;

[0083] σ l =0, l≠δ(t)

[0084] in This means finding the value that makes j the independent variable. The value of j when it reaches its minimum value.

[0085] In one embodiment, the optimal control input is determined based on the selected subsystem model, costate vector, and objective function weight matrix, and the gain matrix of the local feedback is obtained by solving the costate equation.

[0086]

[0087] By adding local feedback control inputs to each agent in a synchronously switching multi-agent system, closed-loop control is formed.

[0088] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0089] A synchronously switching multi-agent system, such as Figure 1 As shown, it contains two isomorphic agents, with the following initial conditions:

[0090]

[0091] In this context, the subscripts 1 and 2 of x correspond to agent 1 and agent 2, respectively.

[0092] The subsystem model parameters for each agent are:

[0093]

[0094] In this context, the subscripts 1 and 2 of A and B correspond to subsystem 1 and subsystem 2 of the agent.

[0095] The objective function weight matrix is:

[0096]

[0097] T = 0.01,

[0098] The optimal subsystem index sequence for each agent in the first ten sampling periods is: 1, 1, 1, 1, 1, 1, 1, 1, 1, 1; the optimal objective function value is J = 7.7678.

[0099] Generate a uniformly distributed random number within the interval (0,1), and determine if it is greater than 0.5. Use this result to generate different subsystem index sequences. Different control inputs are obtained by solving a two-point boundary value problem, such as... Figure 2As shown, adjusting a synchronously switching multi-agent system from the same initial state to the same terminal state produces the following objective function values:

[0100] 1, 1, 1, 1, 1, 1, 1, 2, 1, 1; 8.1579

[0101] 1, 1, 1, 2, 1, 1, 1, 1, 1, 1; 8.2208

[0102] 1, 1, 1, 1, 1, 1, 1, 1, 1, 2; 8.1517

[0103] 1, 1, 1, 1, 1, 1, 2, 1, 1, 2; 8.5857

[0104] 1, 1, 1, 1, 1, 1, 1, 2, 2, 1; 8.5108

[0105] 1, 1, 1, 2, 1, 1, 1, 1, 1, 2; 8.6824

[0106] This invention also provides an optimal control device for a synchronously switching multi-agent system, where each agent is a linearly switching system, each agent contains several subsystems, and at any given time, the agent uses a subsystem model as the evolution model for its state trajectory, with the evolution model switching between multiple subsystems; for example... Figure 3 As shown, the optimal control device includes:

[0107] The intelligent agent subsystem selection module is used to construct the optimal objective function based on the costate vector, the models of each subsystem, and the objective function weight matrix. It calculates the objective function value for each subsystem at any time and selects the subsystem with the smallest objective function value as the evolution model at the current time.

[0108] The agent's optimal control input module is used to determine the optimal control input based on the selected subsystem model, costate vector, and objective function weight matrix.

[0109] It should be noted that the device embodiment shown in this embodiment matches the content of the above method embodiment, and the content of the above method embodiment can be referred to, and will not be repeated here.

[0110] Corresponding to the aforementioned embodiment of an optimal control method for a synchronously switching multi-agent system, the present invention also provides an embodiment of an optimal control device for a synchronously switching multi-agent system.

[0111] See Figure 4 The present invention provides an optimal control device for a synchronously switching multi-agent system, comprising one or more processors, for implementing an optimal control method for a synchronously switching multi-agent system as described in the above embodiments.

[0112] The processor can be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor can be a microprocessor or any conventional processor.

[0113] An embodiment of the optimal control device for a synchronously switching multi-agent system of the present invention can be applied to any device with data processing capabilities, such as a computer. The device embodiment can be implemented in software, hardware, or a combination of both. Taking software implementation as an example, as a logical device, it is formed by the processor of any data-processing device loading the corresponding computer program instructions from non-volatile memory into memory for execution. From a hardware perspective, such as... Figure 4 The diagram shown is a hardware structure diagram of any device with data processing capabilities, which is the optimal control device for a synchronous switching multi-agent system according to the present invention. (Except for...) Figure 4 In addition to the processor, memory, network interface, and non-volatile memory shown, any data processing device in the embodiment may also include other hardware depending on the actual function of the data processing device, which will not be described in detail here.

[0114] The specific implementation process of the functions and roles of each unit in the above device can be found in the implementation process of the corresponding steps in the above method, and will not be repeated here.

[0115] For the device embodiments, since they basically correspond to the method embodiments, the relevant parts can be referred to in the description of the method embodiments. The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of the present invention according to actual needs. Those skilled in the art can understand and implement this without creative effort.

[0116] This invention also provides a computer-readable storage medium storing a program thereon, which, when executed by a processor, implements an optimal control method for a synchronously switching multi-agent system as described in the above embodiments.

[0117] The computer-readable storage medium can be an internal storage unit of any data processing device described in any of the foregoing embodiments, such as a hard disk or memory. The computer-readable storage medium can also be any data processing device, such as a plug-in hard disk, smart media card (SMC), SD card, flash card, etc., equipped on the device. Furthermore, the computer-readable storage medium can include both internal storage units of any data processing device and external storage devices. The computer-readable storage medium is used to store the computer program and other programs and data required by the data processing device, and can also be used to temporarily store data that has been output or will be output.

[0118] The above embodiments are only used to illustrate the design concept and features of the present invention, and their purpose is to enable those skilled in the art to understand the content of the present invention and implement it accordingly. The protection scope of the present invention is not limited to the above embodiments. Therefore, all equivalent changes or modifications made based on the principles and design ideas disclosed in the present invention are within the protection scope of the present invention.

Claims

1. An optimal control method for a synchronously switching multi-agent system, characterized in that, Each agent is a linear switching system, and each agent contains several subsystems. At any given time, the agent uses a subsystem model as the evolution model for its state trajectory, and the evolution model switches between multiple subsystems. The optimal control method includes: Based on the costate vector, the models of each subsystem, and the weight matrix of the objective function, the optimal objective function is constructed. At any time, the objective function value corresponding to each subsystem is calculated, and the subsystem with the smallest objective function value is taken as the evolution model at the current time. The optimal control input is determined based on the selected subsystem model, costate vector, and objective function weight matrix. The evolutionary model of the synchronous switching multi-agent system is as follows: And satisfy , , The total number of subsystems; in , To synchronize the switching of agents in a multi-agent system of dimensional state vector, The total number of intelligent agents; for The derivative with respect to time; for Dimensional control input; For intelligent agents The indivual 3D system matrix; For intelligent agents The indivual A dimensional input matrix; For intelligent agents The One switching variable, and Switching variables are used to characterize the agent. Subsystem switching behavior; The goal of optimal control is to minimize historical states. and terminal status The deviation from the equilibrium point and the quadratic form of control costs, in a finite time domain Within this framework, the objective function for optimal control of a synchronously switching multi-agent system is defined as follows: in Represents the transpose of a vector. , , , for A positive semi-definite matrix; for A positive definite matrix of dimension 1. , ; Solving the optimal control problem of a synchronously switching multi-agent system using the maximum principle yields the costate equations: ， ； in for dimensional costate vector; and satisfying the boundary conditions: ， ； Based on the costate vector, the models of each subsystem, and the weight matrix of the objective function, an optimal objective function is constructed. At any given time, the objective function value for each subsystem is calculated. The subsystem with the smallest objective function value is taken as the evolutionary model for the current time step, including: ， ， ； ； in Indicated by Let be the independent variable, find the value that makes When the minimum value is reached The value is denoted as , is the index of the selected subsystem; , These are model parameters, and the superscript T indicates the transpose operation.

2. The optimal control method for a synchronously switching multi-agent system according to claim 1, characterized in that, The process of constructing the optimal objective function based on the costate vector, the models of each subsystem, and the weight matrix of the objective function, calculating the objective function value for each subsystem at any given time, and selecting the subsystem with the smallest objective function value as the evolutionary model for the current time step is as follows: Step 1: Initialize the weight matrix of the objective function. , , and initial state Initial values ​​of costate variables , , Terminal time Terminal status Given constants As the sampling period; Step 2: Repeat the following steps. Second-rate: The first synchronous switching multi-agent system For each subsystem, calculate the objective function value, obtain the subsystem index corresponding to the minimum value, and use it as the subsystem to be selected; Calculate the costate vector using the selected subsystem model and the objective function weight matrix. And obtain the optimal control input for each agent in the synchronous switching multi-agent system; Calculate the state vector for the next sampling period ; Step 3: Correct the initial value of the costate vector Until the boundary conditions are met, the operating subsystems of the synchronous switching multi-agent system at each moment are determined.

3. The optimal control method for a synchronously switching multi-agent system according to claim 1, characterized in that, The switching time and the selected subsystem model are the same for each agent subsystem in the synchronous switching multi-agent system.

4. The optimal control method for a synchronously switching multi-agent system according to claim 1, characterized in that, The optimal control input is determined based on the selected subsystem model, costate vector, and objective function weight matrix. The gain matrix of the local feedback is obtained by solving the costate equation. ， 。 5. The optimal control method for a synchronously switching multi-agent system according to claim 2, characterized in that, In the specific implementation steps Step 2: Calculate the state vector for the next sampling period: ， ； Step 3: Order for A positive semi-definite matrix; To synchronize the switching of multi-agent systems in Moment 3D state vector; for dimensional vector; Finding the terminal co-mode error Reaching 0 to 1e -3 initial values ​​of costate variables .

6. An optimal control device for a synchronously switching multi-agent system, characterized in that, Each agent is a linear switching system, and each agent contains several subsystems. At any given time, the agent uses a subsystem model as the evolution model for its state trajectory, and the evolution model switches between multiple subsystems. The optimal control device includes: The intelligent agent subsystem selection module is used to construct the optimal objective function based on the costate vector, the models of each subsystem, and the objective function weight matrix. It calculates the objective function value for each subsystem at any time and selects the subsystem with the smallest objective function value as the evolution model at the current time. The agent's optimal control input module is used to determine the optimal control input based on the selected subsystem model, costate vector, and objective function weight matrix. The evolutionary model of the synchronous switching multi-agent system is as follows: And satisfy , , The total number of subsystems; in , To synchronize the switching of agents in a multi-agent system of dimensional state vector, The total number of intelligent agents; for The derivative with respect to time; for Dimensional control input; For intelligent agents The indivual 3D system matrix; For intelligent agents The indivual A dimensional input matrix; For intelligent agents The One switching variable, and Switching variables are used to characterize the agent. Subsystem switching behavior; The goal of optimal control is to minimize historical states. and terminal status The deviation from the equilibrium point and the quadratic form of control costs, in a finite time domain Within this framework, the objective function for optimal control of a synchronously switching multi-agent system is defined as follows: in Represents the transpose of a vector. , , , for A positive semi-definite matrix; for A positive definite matrix of dimension 1. , ; Solving the optimal control problem of a synchronously switching multi-agent system using the maximum principle yields the costate equations: ， ； in for dimensional costate vector; and satisfying the boundary conditions: ， ； Based on the costate vector, the models of each subsystem, and the weight matrix of the objective function, an optimal objective function is constructed. At any given time, the objective function value for each subsystem is calculated. The subsystem with the smallest objective function value is taken as the evolutionary model for the current time step, including: ， ， ； ； in Indicated by Let be the independent variable, find the value that makes When the minimum value is reached The value is denoted as , is the index of the selected subsystem; , These are model parameters, and the superscript T indicates the transpose operation.

7. An optimal control device for a synchronously switching multi-agent system, characterized in that, It includes one or more processors for implementing the optimal control method for a synchronously switching multi-agent system according to any one of claims 1-5.

8. A computer-readable storage medium having a program stored thereon, characterized in that, When executed by the processor, the program is used to implement the optimal control method for a synchronously switching multi-agent system as described in any one of claims 1-5.

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