Event-triggered distributed optimal control system and method for homogeneous multi-agent systems

Abstract

The present invention discloses an event-triggered distributed optimal control system and method for a homogeneous multi-agent system, including providing an event triggering condition that can achieve leader-follower consistency of the multi-agent system under an event-triggered communication mechanism, and the agent checks whether the event triggering condition is satisfied in each sampling period to determine the non-uniform communication moment of the agent; based on the determined non-uniform communication moment of the agent, by minimizing the quadratic objective function and matrix decomposition about the process state cost, control cost and state-control cross cost, an analytical expression of the global optimal distributed control law under the periodic communication mechanism is provided, and a matrix equation group that the feedback matrix of the global optimal distributed control law needs to satisfy is provided, and the feedback control law can be implemented in a distributed manner and can make the global performance index reach the optimal level. The present invention can significantly reduce the number of communications and improve system efficiency and performance.

Description

Technical Field

[0001] The present invention belongs to the cross-technical field of optimal control, non-periodic communication and distributed control, and in particular relates to an event-triggered distributed optimal control system and method for a homogeneous multi-agent system. Background Art

[0002] The formation control of large-scale, wide-area distributed multi-robot systems usually adopts a distributed architecture, which has stronger fault tolerance and robustness than a centralized architecture, and does not require a central control platform with high computing power and high real-time performance and a high-speed, high-throughput communication network to support it. Compared with centralized control, the main defect of distributed control is that it is difficult to ensure global optimality. Multi-robot systems usually face the problems of limited network bandwidth and limited node energy under weak communication conditions and electronic warfare environments. For example, in an electromagnetic spectrum warfare environment, spectrum bandwidth resources may be maliciously occupied by enemy jammers or deceived by bait placement, and the available and safe bandwidth resources allocated to radar, communication, and navigation equipment are very limited. For example, underwater communication networking is affected by the reflection, refraction, and attenuation characteristics of sound waves and multipath effects. In short-distance communications of 1 to 10 km, the bandwidth of underwater acoustic communication is only about tens of thousands of hertz, and in long-distance communications of 10 to 100 km, the bandwidth is only a few thousand hertz. The transmission power of underwater acoustic communication nodes usually needs to be an order of magnitude higher than that of terrestrial wireless communication equipment, and it is difficult to charge or replace batteries for underwater communication nodes, resulting in extremely narrow bandwidth and communication energy shortage in underwater communication scenarios. The event-triggered communication mechanism for multi-robot collaborative control can adjust the communication frequency according to the actual needs of the control task, reduce the occupancy of network bandwidth, and reduce the energy consumption of communication equipment.

[0003] The formation control problem of multi-robot system is a typical distributed control problem of multi-agent system. At present, the research on the optimal control problem of multi-agent system mainly focuses on the quadratic objective function containing process state cost and process control cost. The distributed optimal control problem and the design of event triggering conditions under the quadratic objective function containing process state cost, process control cost and state-control cross cost are rarely involved. The literature (KH Movric and FL Lewis, "Cooperative Optimal Control for Multi-Agent Systems on DirectedGraph Topologies," in IEEE Transactions on Automatic Control, vol. 59, no. 3, pp. 769-774, March 2014.) studied the design method of the weight matrix of the quadratic objective function containing process state cost and process control cost, and gave the necessary conditions for the distributed implementation of the optimal control of general linear multi-agent systems. In the study of event triggering consistency of multi-agent system, the current research work has not yet involved the closed-loop prediction that does not rely on control information interaction. In the literature (W. Hu, L. Liu and G. Feng, Consensus of Linear Multi-Agent Systems by Distributed Event-Triggered Strategy, IEEE Transactions on Cybernetics, vol. 46, no. 1, pp. 148-157, Jan. 2016.), the state prediction of intelligent agents usually adopts open-loop prediction without considering the interaction of control information. Summary of the invention

[0004] The purpose of the present invention is to provide an event-triggered distributed optimal control system and method for a homogeneous multi-agent system in view of the deficiencies in the prior art.

[0005] The object of the present invention is achieved through the following technical solutions: an event-triggered distributed optimal control system for a homogeneous multi-agent system, comprising a distributed optimal control module and an event-triggered consistency protocol module;

[0006] Event-triggered consistency protocol module: It provides event triggering conditions that can achieve leader-follower consistency in the multi-agent system under the event-triggered communication mechanism. The agent checks whether the event triggering conditions are met in each sampling period to determine the non-uniform communication time of the agent;

[0007] Distributed optimal control module: Based on the determined non-uniform communication time of intelligent agents, by minimizing the quadratic objective function and matrix decomposition about the process state cost, control cost and state-control cross cost, the analytical expression of the global optimal distributed control law under the periodic communication mechanism is given, and the matrix equation group that the feedback matrix of the global optimal distributed control law needs to satisfy is given. The feedback control law can be implemented in a distributed manner and can make the global performance indicators reach the optimal level.

[0008] Furthermore, by decomposing the objective function weight matrix and solving the sub-matrix equations, the global optimal distributed control law is obtained; the agents of the homogeneous multi-agent system The model is expressed as:

[0009] (1);

[0010] The multi-agent system model is expressed as:

[0011] (2);

[0012] in For multi-agent systems Moment dimensional state vector, the superscript T indicates the transpose operation; , For intelligent agents of dimensional state vector; the number of agents in a multi-agent system is N+1; for Dimensional control input, For intelligent agents of Dimensional control input, and The intelligent dimensional system matrix and dimensional control matrix, for dimensional identity matrix, represents the Kronecker product;

[0013] The goal of optimal control of a multi-agent system is to minimize the process state cost. and control costs and state-control crossover cost ; Define the infinite time quadratic objective function of the homogeneous multi-agent system as:

[0014] (3);

[0015] Among them, the weight matrix for The semi-positive definite matrix of for Matrix; weight matrix for A positive definite matrix of

[0016] The global optimal control law that minimizes the quadratic objective function can be obtained through the maximum principle:

[0017] (4);

[0018] Positive definite matrix is the only solution that satisfies the following matrix Riccati equation:

[0019] (5);

[0020] If the matrix , , Decomposed into the following form:

[0021] ; ; (6);

[0022] Design sub-matrix Satisfies the matrix equation system:

[0023] ; ; (7);

[0024] (8);

[0025] in is the coupling coefficient, is the Laplace matrix of the multi-agent system, that is

[0026] ; (9);

[0027] in , , Represents the communication topology of a multi-agent system. If the agent Towards an Agent The agent that sends state information is called It is smart Neighbors and ,otherwise ;gather To the intelligent agent The set of neighboring agents;

[0028] The matrix Riccati equation becomes:

[0029] (10);

[0030] That is, the weight matrix satisfy:

[0031] (11);

[0032] The global optimal distributed control law is Distributed computing and implementation are possible, namely:

[0033] (12);

[0034] in is the local feedback matrix, the agent The local feedback control law is expressed as:

[0035] (13);

[0036] in, Representing an Agent Neighbor Agent Status;

[0037] The closed-loop multi-agent system model with local feedback is expressed as:

[0038] (14).

[0039] Furthermore, the leader-follower consistency of the multi-agent system is achieved through the leader-follower communication topology and local feedback control; i.e.

[0040] (15);

[0041] in is the leader state; intelligent agent The local feedback control law is expressed as:

[0042] (16);

[0043] in, , , Represents a leader-follower communication topology. If the leader Send status information, then ,otherwise ;

[0044] When the sub-matrix satisfy:

[0045] (17);

[0046] The matrix ; Submatrix Satisfying the matrix equations (8) and (11), the distributed control law is relative to the quadratic objective function is the best.

[0047] Furthermore, the non-uniform communication moments are calculated through event-triggered communication conditions, and the distributed event triggering conditions and the thresholds that decay over time are constructed through state estimation errors to achieve leader-follower consistency in multi-agent systems;

[0048] Constructing an Agent Event trigger conditions:

[0049] (18);

[0050] The state estimation error is:

[0051] (19);

[0052] in It is an intelligent agent The state estimate, threshold is a decreasing function that decays to 0 over time, that is, satisfies

[0053] (20);

[0054] When checking the event trigger condition (18) at the set sampling frequency, if If true, the event is triggered, and the triggering time is recorded as ; When the agent When the event is triggered, the agent Send its own state information to its neighboring agents, and obtain the local feedback control law of agent j through formula (16); when agent When the event of is not triggered, the agent Do not send information about their own state to their neighboring agents.

[0055] Furthermore, when the agent's event is not triggered, the agent's neighbors estimate the agent's state through a closed-loop prediction method that does not rely on real-time control information; The system model is based on the cycle Performing first-order discretization, we get:

[0056] twenty one;

[0057] Agent Neighbor Agent , that is, accepting the agent Status Information The intelligent agent, based on the intelligent agent Current moment and the previous moment The status information is obtained:

[0058] (twenty two);

[0059] When the intelligent At the triggering moment During the period when the event is not triggered, the agent The agent is estimated by the following equation state, i.e. using For Agents Closed-loop prediction of the state;

[0060] (twenty three); (twenty four);

[0061] in is a positive integer, For intelligent agents No. A trigger moment;

[0062] When the intelligent When the event of is not triggered, its neighboring agent The control law is:

[0063] (25)

[0064] The collection Intelligent Agent is the set of agents that are neighbors and triggered, Intelligent Agent is a neighbor and the event does not trigger the set of agents, is the state of agent l.

[0065] Furthermore, the specific implementation steps are as follows:

[0066] Step 1: Initialize the agent model matrix , ,number , the weight matrix of the objective function , , and the initial state , given a constant As the sampling period; determine the Laplace matrix based on the topological structure of the multi-agent communication network ;

[0067] Step 2: Solve through the matrix equations (7)(8)(11) Get the feedback matrix ;

[0068] Step 3: Loop through the following steps until :

[0069] For multi-agent systems An intelligent agent, , receiving neighbor status information , ;

[0070] Estimating neighbor agents that have not sent state information Status , ;

[0071] Calculate (13) and (25) to obtain the distributed control law and ;

[0072] Check the event triggering condition (18), and if the condition is met, send status information to the neighbor , if the condition is not met, it will not be sent.

[0073] The present invention also provides an event-triggered distributed optimal control method for a homogeneous multi-agent system, comprising:

[0074] The event triggering conditions that can achieve leader-follower consistency in the multi-agent system under the event-triggered communication mechanism are given. The agents check whether the event triggering conditions are met in each sampling period to determine the non-uniform communication time of the agents.

[0075] Based on the determined non-uniform communication moments of intelligent agents, the analytical expression of the global optimal distributed control law under the periodic communication mechanism is given by minimizing the quadratic objective function and matrix decomposition about the process state cost, control cost and state-control cross cost. The matrix equation group that the feedback matrix of the global optimal distributed control law needs to satisfy is also given. The feedback control law can be implemented in a distributed manner and can make the global performance indicators reach the optimal level.

[0076] The present invention also provides an electronic device, comprising a memory and a processor, wherein the memory is coupled to the processor; wherein the memory is used to store program data, and the processor is used to execute the program data to implement the above-mentioned event-triggered distributed optimal control method for a homogeneous multi-agent system.

[0077] The present invention also provides a computer-readable storage medium on which a computer program is stored. When the program is executed by a processor, the event-triggered distributed optimal control method of the above-mentioned homogeneous multi-agent system is implemented.

[0078] The present invention also provides a computer program product, including a computer program, which, when executed by a processor, implements the above-mentioned event-triggered distributed optimal control method for a homogeneous multi-agent system.

[0079] Compared with the prior art, the beneficial effects of the present invention are: providing a set of matrix equations that need to be satisfied for distributed computing of the global optimal control law and distributed event triggering conditions for achieving consistency, and further providing a closed-loop prediction method for the state of the intelligent agent, thereby greatly reducing the number of communications and improving system efficiency and performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0080] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings required for use in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings in the following description are only some embodiments of the present invention. For ordinary technicians in this field, other accompanying drawings can be obtained based on these accompanying drawings without paying creative labor.

[0081] Figure 1 It is a schematic diagram of the structure of an event-triggered multi-agent system;

[0082] Figure 2 It is the position trajectory diagram of agents 0-3;

[0083] Figure 3 is the velocity trajectory diagram of agent 0-3;

[0084] Figure 4 is the acceleration trajectory of agent 0-3;

[0085] Figure 5 is the communication time distribution of agent 1-2;

[0086] Figure 6 It is a schematic diagram of an electronic device provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0087] The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and cannot be used to limit the protection scope of the present invention. The present invention is described in detail below in conjunction with the accompanying drawings. In the absence of conflict, the features in the following embodiments and implementations can be combined with each other.

[0088] An event-triggered distributed optimal control system for a homogeneous multi-agent system of the present invention comprises a distributed optimal control module and an event-triggered consistency protocol module;

[0089] Event-triggered consistency protocol module: It provides event triggering conditions that can achieve leader-follower consistency in the multi-agent system under the event-triggered communication mechanism. The agent checks whether the event triggering conditions are met in each sampling period to determine the non-uniform communication time of the agent;

[0090] Distributed optimal control module: Based on the determined non-uniform communication time of intelligent agents, by minimizing the quadratic objective function and matrix decomposition about the process state cost, control cost and state-control cross cost, the analytical expression of the global optimal distributed control law under the periodic communication mechanism is given, and the matrix equation group that the feedback matrix of the global optimal distributed control law needs to satisfy is given. The feedback control law can be implemented in a distributed manner and can make the global performance indicators reach the optimal level.

[0091] Specifically, the global optimal distributed control law is obtained by decomposing the objective function weight matrix and solving the sub-matrix equation group; the agents of the homogeneous multi-agent system The model is expressed as:

[0092] (1);

[0093] The multi-agent system model is expressed as:

[0094] (2);

[0095] in For multi-agent systems Moment dimensional state vector, the superscript T indicates the transpose operation; , For intelligent agents of dimensional state vector; the number of agents in a multi-agent system is N+1; for Dimensional control input, For intelligent agents of Dimensional control input, and The intelligent dimensional system matrix and dimensional control matrix, for dimensional identity matrix, represents the Kronecker product;

[0096] The goal of optimal control of a multi-agent system is to minimize the process state cost. and control costs and state-control crossover cost ; Define the infinite time quadratic objective function of the homogeneous multi-agent system as:

[0097] (3);

[0098] Among them, the weight matrix for The semi-positive definite matrix of for Matrix; weight matrix for A positive definite matrix of

[0099] The global optimal control law that minimizes the quadratic objective function can be obtained through the maximum principle:

[0100] (4);

[0101] Positive definite matrix is the only solution that satisfies the following matrix Riccati equation:

[0102] (5);

[0103] If the matrix , , Decomposed into the following form:

[0104] ; ; (6);

[0105] Design sub-matrix Satisfies the matrix equation system:

[0106] ; ; (7);

[0107] (8);

[0108] in is the coupling coefficient, is the Laplace matrix of the multi-agent system, that is

[0109] ; (9);

[0110] in , , Represents the communication topology of a multi-agent system. If the agent Towards an Agent The agent that sends state information is called It is smart Neighbors and ,otherwise ;gather To the intelligent agent The set of neighboring agents;

[0111] The matrix Riccati equation becomes:

[0112] (10);

[0113] That is, the weight matrix satisfy:

[0114] (11);

[0115] The global optimal distributed control law is Distributed computing and implementation are possible, namely:

[0116] (12);

[0117] in is the local feedback matrix, the agent The local feedback control law is expressed as:

[0118] (13);

[0119] in, Representing an Agent Neighbor Agent Status;

[0120] The closed-loop multi-agent system model with local feedback is expressed as:

[0121] (14).

[0122] Specifically, the leader-follower consistency of the multi-agent system is achieved through the leader-follower communication topology and local feedback control; that is,

[0123] (15);

[0124] in is the leader state; intelligent agent The local feedback control law is expressed as:

[0125] (16);

[0126] in, , , Represents a leader-follower communication topology. If the leader Send status information, then ,otherwise ;

[0127] When the sub-matrix satisfy:

[0128] (17);

[0129] The matrix ; Submatrix Satisfying the matrix equations (8) and (11), the distributed control law is relative to the quadratic objective function is the best.

[0130] Specifically, the non-uniform communication moments are calculated through event-triggered communication conditions, and the distributed event triggering conditions and thresholds that decay over time are constructed through state estimation errors to achieve leader-follower consistency in multi-agent systems;

[0131] Constructing an Agent Event trigger conditions:

[0132] (18);

[0133] The state estimation error is:

[0134] (19);

[0135] in It is an intelligent agent The state estimate, threshold is a decreasing function that decays to 0 over time, that is, satisfies

[0136] (20);

[0137] When checking the event trigger condition (18) at the set sampling frequency, if If true, the event is triggered, and the triggering time is recorded as ; When the agent When the event is triggered, the agent Send its own state information to its neighboring agents, and obtain the local feedback control law of agent j through formula (16); when agent When the event of is not triggered, the agent Do not send information about their own state to their neighboring agents.

[0138] Specifically, when the agent's event is not triggered, the agent's neighbors estimate the agent's state through a closed-loop prediction method that does not rely on real-time control information; The system model is based on the cycle Performing first-order discretization, we get:

[0139] twenty one;

[0140] Agent Neighbor Agent , that is, accepting the agent Status Information The intelligent agent, based on the intelligent agent Current moment and the previous moment The status information is obtained:

[0141] (twenty two);

[0142] When the intelligent At the triggering moment During the period when the event is not triggered, the agent The agent is estimated by the following equation state, i.e. using For Agents Closed-loop prediction of the state;

[0143] (twenty three); (twenty four);

[0144] in is a positive integer, For intelligent agents No. A trigger moment;

[0145] When the intelligent When the event of is not triggered, its neighboring agent The control law is:

[0146] (25)

[0147] The collection Intelligent Agent is the set of agents that are neighbors and triggered, Intelligent Agent is a neighbor and the event does not trigger the set of agents, is the state of agent l.

[0148] Specifically, the implementation steps are as follows:

[0149] Step 1: Initialize the agent model matrix , ,number , the weight matrix of the objective function , , and the initial state , given a constant As the sampling period; determine the Laplace matrix based on the topological structure of the multi-agent communication network ;

[0150] Step 2: Solve through the matrix equations (7)(8)(11) Get the feedback matrix ;

[0151] Step 3: Loop through the following steps until :

[0152] For multi-agent systems An intelligent agent, , receiving neighbor status information , ;

[0153] Estimating neighbor agents that have not sent state information Status , ;

[0154] Calculate (13) and (25) to obtain the distributed control law and ;

[0155] Check the event triggering condition (18), and if the condition is met, send status information to the neighbor , if the condition is not met, it will not be sent.

[0156] The present invention also provides an event-triggered distributed optimal control method for a homogeneous multi-agent system, comprising:

[0157] The event triggering conditions that can achieve leader-follower consistency in the multi-agent system under the event-triggered communication mechanism are given. The agents check whether the event triggering conditions are met in each sampling period to determine the non-uniform communication time of the agents.

[0158] Based on the determined non-uniform communication moments of intelligent agents, the analytical expression of the global optimal distributed control law under the periodic communication mechanism is given by minimizing the quadratic objective function and matrix decomposition about the process state cost, control cost and state-control cross cost. The matrix equation group that the feedback matrix of the global optimal distributed control law needs to satisfy is also given. The feedback control law can be implemented in a distributed manner and can make the global performance indicators reach the optimal level.

[0159] It should be noted that the method embodiment shown in this embodiment matches the content of the above-mentioned system embodiment, and the content of the above-mentioned system embodiment can be referred to, which will not be repeated here.

[0160] The implementation of the present invention will be described in detail below with reference to the accompanying drawings.

[0161] A multi-agent system, such as Figure 1 As shown, it contains 4 isomorphic agents, and the model of each agent is:

[0162] , ;

[0163] The initial conditions are:

[0164] , , , ; Agents 0-3 have three states: position, velocity, and acceleration;

[0165] The communication topology of a multi-agent system is as follows: Figure 1 As shown:

[0166] , ;

[0167] Select: , , , we can calculate:

[0168] , ,

[0169] Select: , sampling period: Agent 0 is the leader and continuously sends status information to agent 1. Agents 1 and 2 intermittently send their own status information to their neighbors, agents 2 and 3. The status trajectories of agents 0-3 are shown in Figure 2-Figure 4 As shown, the communication time is Figure 5 As shown in the figure, the triggering times of agents 1 and 2 are 12 and 17 respectively. Compared with the 80 communication moments of periodic sampling, the use of event triggering and closed-loop prediction can reduce the number of communications by more than 80%.

[0170] The present invention also provides an electronic device, such as Figure 6 As shown, it includes a memory and a processor, and the memory is coupled to the processor; wherein the memory is used to store program data, and the processor is used to execute the program data to implement the above-mentioned event-triggered distributed optimal control method for a homogeneous multi-agent system.

[0171] It should be noted that, in addition to Figure 6In addition to the memory and processor shown, the electronic device may also include other hardware according to its actual functions, which will not be described in detail.

[0172] The present invention also provides a computer-readable storage medium on which a computer program is stored. When the program is executed by a processor, the event-triggered distributed optimal control method of the above-mentioned homogeneous multi-agent system is implemented.

[0173] The present invention also provides a computer program product, including a computer program, which, when executed by a processor, implements the above-mentioned event-triggered distributed optimal control method for a homogeneous multi-agent system.

[0174] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Moreover, the present application may adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program codes.

[0175] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0176] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture including an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0177] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0178] The above embodiments are only used to illustrate the design ideas 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, any equivalent changes or modifications made based on the principles and design ideas disclosed by the present invention are within the protection scope of the present invention.

Claims

1. An event-triggered distributed optimal control system for a homogeneous multi-agent system, characterized in that: Includes distributed optimal control module and event-triggered consistency protocol module; Event-triggered consistency protocol module: It provides event triggering conditions that can achieve leader-follower consistency in the multi-agent system under the event-triggered communication mechanism. The agent checks whether the event triggering conditions are met in each sampling period to determine the non-uniform communication time of the agent; Distributed optimal control module: Based on the determined non-uniform communication time of the intelligent agent, by minimizing the quadratic objective function and matrix decomposition about the process state cost, control cost and state-control cross cost, the analytical expression of the global optimal distributed control law under the periodic communication mechanism is given, and the matrix equation group that the feedback matrix of the global optimal distributed control law needs to satisfy is given. The feedback control law can be implemented in a distributed manner and can optimize the global performance indicators, including: The global optimal distributed control law is obtained by decomposing the objective function weight matrix and solving the sub-matrix equation group; the agents of the homogeneous multi-agent system The model is expressed as: （1）； The multi-agent system model is expressed as: （2）； in For multi-agent systems Moment dimensional state vector, the superscript T indicates the transpose operation; , For intelligent agents of dimensional state vector; the number of agents in a multi-agent system is N+1 ; for Dimensional control input, For intelligent agents of Dimensional control input, and The intelligent dimensional system matrix and dimensional control matrix, for dimensional identity matrix, represents the Kronecker product; The goal of optimal control of a multi-agent system is to minimize the process state cost. and control costs and state-control crossover cost ; Define the infinite time quadratic objective function of the homogeneous multi-agent system as: （3）； Among them, the weight matrix for The semi-positive definite matrix of for Matrix; weight matrix for A positive definite matrix of ; The global optimal control law that minimizes the quadratic objective function can be obtained through the maximum principle: （4）； Positive definite matrix is the only solution that satisfies the following matrix Riccati equation: （5）； If the matrix , , Decomposed into the following form: ； ； （6）； Design sub-matrix Satisfies the matrix equation system: ； ； （7）； （8）； in is the coupling coefficient, is the Laplace matrix of the multi-agent system, that is ； （9）； in , , Represents the communication topology of a multi-agent system. If the agent Towards an Agent The agent that sends state information is called It is smart Neighbors and ,otherwise ;gather To the intelligent agent The set of neighboring agents; The matrix Riccati equation becomes: （10）； That is, the weight matrix satisfy: （11）； The global optimal distributed control law is Distributed computing and implementation are possible, namely: （12）； in is the local feedback matrix, the agent The local feedback control law is expressed as: （13）； in, Representing an Agent Neighbor Agent Status; The closed-loop multi-agent system model with local feedback is expressed as: （14）。 2. The event-triggered distributed optimal control system of a homogeneous multi-agent system according to claim 1, characterized in that: Leader-follower consistency of multi-agent systems is achieved through leader-follower communication topology and local feedback control; i.e. （15）； in is the leader state; intelligent agent The local feedback control law is expressed as: （16）； in, , , Represents a leader-follower communication topology. If the leader Send status information, then ,otherwise ; When the sub-matrix satisfy: （17）； The matrix ; Submatrix Satisfying the matrix equations (8) and (11), the distributed control law is relative to the quadratic objective function is the best.

3. The event-triggered distributed optimal control system of a homogeneous multi-agent system according to claim 2, characterized in that: The non-uniform communication moments are calculated through event-triggered communication conditions, and the distributed event triggering conditions and thresholds that decay over time are constructed through state estimation errors to achieve leader-follower consistency in multi-agent systems. Constructing an Agent Event trigger conditions: （18）； The state estimation error is: （19）； in It is an intelligent agent The state estimate, threshold is a decreasing function that decays to 0 over time, that is, satisfies （20）； When checking the event trigger condition (18) at the set sampling frequency, if If true, the event is triggered, and the triggering time is recorded as ; When the agent When the event is triggered, the agent Send its own state information to its neighboring agents, and obtain the agent through formula (16) j The local feedback control law represents that when the agent When the event of is not triggered, the agent Do not send information about their own state to their neighboring agents.

4. The event-triggered distributed optimal control system of a homogeneous multi-agent system according to claim 3, characterized in that: When the agent's event is not triggered, the agent's neighbors estimate the agent's state through a closed-loop prediction method that does not rely on real-time control information; The system model is based on the cycle Performing first-order discretization, we get: 21； Agent Neighbor Agent , that is, accepting the agent Status Information The intelligent agent, based on the intelligent agent Current moment and the previous moment The status information is obtained: （22）； When the intelligent At the triggering moment During the period when the event is not triggered, the agent The agent is estimated by the following equation state, i.e. using For Agents Closed-loop prediction of the state; （23）； （24）； in is a positive integer, For intelligent agents No. A trigger moment; When the intelligent When the event of is not triggered, its neighboring agent The control law is: （25） The collection Intelligent Agent is the set of agents that are neighbors and triggered, Intelligent Agent is a neighbor and the event does not trigger the set of agents, For intelligent agents l status.

5. The event-triggered distributed optimal control system of a homogeneous multi-agent system according to claim 4, characterized in that: The specific implementation steps are as follows: Step 1: Initialize the agent model matrix , ,number , the weight matrix of the objective function , , and the initial state , given a constant As sampling period; Determine the Laplace matrix based on the topology of the multi-agent communication network ; Step 2: Solve through the matrix equations (7)(8)(11) Get the feedback matrix ; Step 3: Loop through the following steps until : For multi-agent systems An intelligent agent, , receiving neighbor status information , ; Estimating neighbor agents that have not sent state information Status , ; Calculate (13) and (25) to obtain the distributed control law and ; Check the event triggering condition (18), and if the condition is met, send status information to the neighbor , if the condition is not met, it will not be sent.

6. An event-triggered distributed optimal control method for a homogeneous multi-agent system, characterized in that: include: The event triggering conditions that can achieve leader-follower consistency in the multi-agent system under the event-triggered communication mechanism are given. The agents check whether the event triggering conditions are met in each sampling period to determine the non-uniform communication time of the agents. Based on the non-uniform communication time of the determined intelligent agent, the analytical expression of the global optimal distributed control law under the periodic communication mechanism is given by minimizing the quadratic objective function and matrix decomposition about the process state cost, control cost and state-control cross cost, and the matrix equation group that the feedback matrix of the global optimal distributed control law needs to satisfy is given. The feedback control law can be implemented in a distributed manner and can optimize the global performance indicators, including: The global optimal distributed control law is obtained by decomposing the objective function weight matrix and solving the sub-matrix equation group; the agents of the homogeneous multi-agent system The model is expressed as: （1）； The multi-agent system model is expressed as: （2）； in For multi-agent systems Moment dimensional state vector, the superscript T indicates the transpose operation; , For intelligent agents of dimensional state vector; the number of agents in a multi-agent system is N+1 ; for Dimensional control input, For intelligent agents of Dimensional control input, and The intelligent dimensional system matrix and dimensional control matrix, for dimensional identity matrix, represents the Kronecker product; The goal of optimal control of a multi-agent system is to minimize the process state cost. and control costs and state-control crossover cost ; Define the infinite time quadratic objective function of the homogeneous multi-agent system as: （3）； Among them, the weight matrix for The semi-positive definite matrix of for Matrix; weight matrix for A positive definite matrix of The global optimal control law that minimizes the quadratic objective function can be obtained through the maximum principle: （4）； Positive definite matrix is the only solution that satisfies the following matrix Riccati equation: （5）； If the matrix , , Decomposed into the following form: ； ； （6）； Design sub-matrix Satisfies the matrix equation system: ； ； （7）； （8）； in is the coupling coefficient, is the Laplace matrix of the multi-agent system, that is ； （9）； in , , Represents the communication topology of a multi-agent system. If the agent Towards an Agent The agent that sends state information is called It is smart Neighbors and ,otherwise ;gather To the intelligent agent The set of neighboring agents; The matrix Riccati equation becomes: （10）； That is, the weight matrix satisfy: （11）； The global optimal distributed control law is Distributed computing and implementation are possible, namely: （12）； in is the local feedback matrix, the agent The local feedback control law is expressed as: （13）； in, Representing an Agent Neighbor Agent Status; The closed-loop multi-agent system model with local feedback is expressed as: （14）。 7. An electronic device comprising a memory and a processor, characterized in that: The memory is coupled to the processor; wherein, the memory is used to store program data, and the processor is used to execute the program data to implement the event-triggered distributed optimal control method of a homogeneous multi-agent system as described in claim 6.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by the processor, it implements the event-triggered distributed optimal control method for a homogeneous multi-agent system as described in claim 6.

9. A computer program product, comprising a computer program, characterized in that When the computer program is executed by a processor, it implements the event-triggered distributed optimal control method for a homogeneous multi-agent system as described in any one of claim 6.

Images