CN119310860B - Event-triggered distributed optimal control system and method for isomorphic multi-agent system - Google Patents
Event-triggered distributed optimal control system and method for isomorphic multi-agent system Download PDFInfo
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Abstract
本发明公开了一种同构多智能体系统的事件触发分布式最优控制系统及方法，包括给出事件触发通信机制下可实现多智能体系统领导者‑跟随一致性的事件触发条件，智能体每个采样周期均检查事件触发条件是否满足，以确定智能体的非均匀通信时刻；基于确定的智能体的非均匀通信时刻，通过最小化关于过程状态代价、控制代价和状态‑控制交叉代价的二次目标函数和矩阵分解，给出周期通信机制下全局最优分布式控制律的解析表达式，并给出全局最优分布式控制律的反馈矩阵需满足的矩阵方程组，反馈控制律可分布式实施且能使全局性能指标达到最优。本发明可以大幅度减少通信次数，提高系统效率和性能。
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 optimize the global performance index. The present invention can significantly reduce the number of communications and improve system efficiency and performance.
Description
Technical Field
The invention belongs to the technical field of intersection of optimal control, aperiodic communication and distributed control, and particularly relates to an event-triggered distributed optimal control system and method of an isomorphic multi-agent system.
Background
The formation control of the large-scale and wide-area distributed multi-robot system generally adopts a distributed architecture, has stronger fault tolerance capability and robustness than a centralized architecture, and does not need a large-scale and high-real-time central control platform and a high-speed and high-throughput communication network to support. The main drawback of distributed control, as opposed to centralized control, is the difficulty in guaranteeing global optimality. The multi-robot system generally faces the problems of limited network bandwidth and limited node energy under weak communication conditions and electronic warfare environments, for example, spectrum bandwidth resources can be maliciously occupied by enemy jammers or decoy deception in electromagnetic spectrum warfare environments, and available and safe bandwidth resources allocated to radar, communication and navigation equipment are very limited. For example, underwater communication networking is affected by acoustic reflection, refraction and attenuation characteristics and multipath effects, the bandwidth of underwater communication is only about tens of thousands of hertz in short-distance communication of 1-10 km, and the bandwidth is only a few kilohertz in long-distance communication of 10-100 km. The transmission power of the underwater acoustic communication node is usually an order of magnitude higher than that of the land wireless communication device, and the underwater communication node is difficult to charge or replace a battery, so that the bandwidth of the underwater communication scene is extremely narrow and the communication energy is short. The event triggering communication mechanism for the cooperative control of multiple robots can adjust the communication frequency according to the actual requirements of control tasks, reduce the occupation of network bandwidth and reduce the energy consumption of communication equipment.
The multi-robot system formation control problem is a typical multi-intelligent system distributed control problem. The current research on the optimal control problem of the multi-agent system mainly aims at a secondary objective function containing process state cost and process control cost, and the distributed optimal control problem and the event triggering condition design problem thereof under the secondary objective function containing process state cost and process control cost and state-control cross cost are rarely involved. Literature (K. H. Movric and F. L. Lewis, "Cooperative Optimal Control for Multi-Agent Systems on Directed Graph Topologies," in IEEE Transactions on Automatic Control, vol. 59, no. 3, pp. 769-774, March 2014.) explores a method for designing a weight matrix of a quadratic objective function containing process state costs and process control costs, giving the necessary conditions for the distributed implementation of optimal control of a general linear multi-agent system. In the research of multi-agent system event triggering consistency, the current research work does not relate to closed-loop prediction independent of control information interaction. The state prediction of agents in 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.） typically employs open loop prediction that does not take into account control information interactions.
Disclosure of Invention
The invention aims at overcoming the defects of the prior art and provides an event-triggered distributed optimal control system and method for an isomorphic multi-agent system.
The invention aims at realizing the technical scheme that the event triggering distributed optimal control system of the isomorphic multi-agent system comprises a distributed optimal control module and an event triggering consistency protocol module;
the event triggering consistency protocol module is used for giving event triggering conditions which can realize the consistency of a leader-following of the multi-agent system under an event triggering communication mechanism, and checking whether the event triggering conditions are met or not in each sampling period of the agent so as to determine the non-uniform communication moment of the agent;
And the distributed optimal control module is used for giving an analytical expression of the global optimal distributed control law under a periodic communication mechanism and a matrix equation set which needs to be met by a feedback matrix of the global optimal distributed control law based on the determined non-uniform communication moment of the intelligent agent by minimizing a secondary objective function and matrix decomposition about process state cost, control cost and state-control crossover cost, wherein the feedback control law can be implemented in a distributed manner and can enable global performance indexes to be optimal.
Further, the global optimal distributed control law is obtained through objective function weight matrix decomposition and submatrix equation set solution, and the intelligent agent of the isomorphic multi-intelligent agent systemIs expressed as:
(1);
The multi-agent system model is expressed as:
(2);
Wherein the method comprises the steps of In a multi-agent systemTime of dayA dimension state vector, superscript T, represents a transpose operation;, Is an intelligent body A kind of electronic deviceThe number of the intelligent agents in the multi-intelligent system is N+1; Is that A dimension control input is provided to the control system,Is an intelligent bodyA kind of electronic deviceA dimension control input is provided to the control system,AndRespectively of intelligent bodiesView system matrixA control matrix of dimensions is provided,Is thatThe dimensional identity matrix is used to determine the identity of the object,Represents the kronecker product;
the goal of optimal control of a multi-agent system is to minimize process state costs And control costAnd state-control cross costDefining an infinite time quadratic objective function of the isomorphic multi-agent system as:
(3);
Wherein the weight matrix Is thatA weight matrixIs thatMatrix of weightsIs thatIs a positive definite matrix of (2);
The global optimal control law for minimizing the secondary objective function can be obtained through the principle of maximum value:
(4);
positive definite matrix Is the only solution that satisfies the following matrix licarpa's equation:
(5);
If matrix ,,The method is divided into the following forms:
;;(6);
Design of submatrices The system of matrix equations is satisfied:
;;(7);
(8);
Wherein the method comprises the steps of As a result of the coupling coefficient,Laplacian matrix for multi-agent systems, i.e
;(9);
Wherein the method comprises the steps of,,Representing communication topology of a multi-agent system if agentsTo intelligent bodyThe sending state information is called as intelligent agentIs intelligentNeighbor and of (2)OtherwiseCollection ofTo intelligent bodyA set of neighbor agents;
The matrix licarpa's equation becomes:
(10);
Instant weight matrix The method meets the following conditions:
(11);
Global optimal distributed control law Distributed computing and implementation is possible, namely:
(12);
Wherein the method comprises the steps of For local feedback matrix, agentThe local feedback control law of (2) is expressed as:
(13);
wherein, Representing an agentNeighbor agent of (a)State of (2);
The closed loop multi-agent system model of local feedback is expressed as:
(14)。
further, leader-follower consistency of multi-agent systems through leader-follower communication topology and local feedback control
(15);
Wherein the method comprises the steps ofIs in the state of a leader and is an intelligent agentIs represented by a local feedback control law:
(16);
wherein, ,,Representing leader-follow communication topology if the leader is directed to an agentTransmitting status informationOtherwise;
When submatrixThe method meets the following conditions:
(17);
Wherein the matrix Sub-matrixSatisfying the matrix equation sets (8) and (11), the distributed control law is relatively quadratic objective functionIs optimal.
Further, calculating non-uniform communication time through event triggering communication conditions, constructing distributed event triggering conditions and a threshold value of decay with time through state estimation errors, and realizing leader-follower consistency of the multi-agent system;
Construction intelligent body Event trigger conditions of (2):
(18);
Wherein the state estimation error:
(19);
Wherein the method comprises the steps of Is an intelligent bodyState estimation value, threshold value of (2)As a decreasing function of decay to 0 over time, i.e. to satisfy
(20);
Checking event triggering conditions (18) at a set sampling frequency ifIf true, triggering the event, and recording the triggering time asWhen the agent isIs triggered by an event of (a) an agentTransmitting self state information to the neighbor agent, obtaining local feedback control law expression of agent j through formula (16), when agentWhen the event of (a) is not triggeredAnd does not send self state information to its neighbor agents.
Further, when the event of the intelligent agent is not triggered, the neighbor of the intelligent agent estimates the state of the intelligent agent by a closed-loop prediction method independent of real-time control informationIn cycles of the system model of (2)Performing first-order discretization to obtain:
21;
Intelligent body Neighbor agent of (a)Namely, receiving the agentStatus informationAccording to the agent of (2)At the current timeAnd the previous timeThe status information of (2) is obtained:
(22);
When the intelligent agent At the moment of triggeringDuring the time period that the post event is not triggered, the agentThe agent is estimated by the following equationState of (i.e. use of)For intelligent bodyPerforming closed-loop prediction of the state of (2);
(23);(24);
Wherein the method comprises the steps of Is a positive integer which is used for the preparation of the high-voltage power supply,Is an intelligent bodyIs the first of (2)Triggering time;
When the intelligent agent When the event of (a) is not triggered, its neighbor agentThe control law of (2) is:
(25)
wherein the aggregate Based on intelligent agentsIs a set of neighbor and triggered agents,Based on intelligent agentsIs a neighbor and the event does not trigger the set of agents,Is the state of agent l.
Further, the specific implementation steps are as follows:
Step1 initializing an agent model matrix 、Number ofWeight matrix of objective function、、And initial stateGiven a constantDetermining Laplacian matrix according to multi-agent communication network topology structure as sampling period;
Step 2 solving through the matrix equation sets (7) (8) (11)Obtaining a feedback matrix;
Step 3, circularly executing the following steps until:
Second to multiple agent systemThe intelligent agent is used for controlling the intelligent agent,Accepting neighbor state information,;
Neighbor agents that estimate non-transmitted state informationState of (2),;
Calculation (13) and (25) to obtain a distributed control lawAnd;
Checking event triggering conditions (18), and if the conditions are satisfied, transmitting status information to the neighborsAnd if the condition is not satisfied, not transmitting.
The invention also provides an event-triggered distributed optimal control method of the isomorphic multi-agent system, which comprises the following steps:
Giving event triggering conditions capable of realizing the consistence of a leader-follow of a multi-agent system under an event triggering communication mechanism, and checking whether the event triggering conditions are met or not in each sampling period of an agent so as to determine non-uniform communication time of the agent;
Based on the determined non-uniform communication time of the intelligent agent, by minimizing a secondary objective function and matrix decomposition about process state cost, control cost and state-control crossover cost, an analytical expression of a globally optimal distributed control law under a periodic communication mechanism is given, and a matrix equation set which needs to be satisfied by a feedback matrix of the globally optimal distributed control law is given, wherein the feedback control law can be implemented in a distributed manner and can enable global performance indexes to be optimal.
The invention also provides electronic equipment, which comprises a memory and a processor, wherein the memory is coupled with the processor, the memory is used for storing program data, and the processor is used for executing the program data to realize the event triggering distributed optimal control method of the isomorphic multi-agent system.
The invention also provides a computer readable storage medium, on which a computer program is stored, which when executed by a processor implements an event-triggered distributed optimal control method of an isomorphic multi-agent system as described above.
The invention also provides a computer program product, which comprises a computer program, wherein the computer program realizes the event-triggered distributed optimal control method of the isomorphic multi-agent system when being executed by a processor.
Compared with the prior art, the method has the beneficial effects that the method provides a matrix equation set which can be calculated in a distributed mode by the global optimal control law and needs to be satisfied, realizes the distributed event triggering condition of consistency, and further provides a closed-loop prediction method of the state of the intelligent agent, so that the communication times are greatly reduced, and the system efficiency and performance are improved.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings that are needed in the description of the embodiments will be briefly described below, it being obvious that the drawings in the following description are only some embodiments of the present invention, and that other drawings may be obtained according to these drawings without inventive effort to a person skilled in the art.
FIG. 1 is a schematic diagram of an event-triggered multi-intelligent system architecture;
FIG. 2 is a diagram of the location trajectories of agents 0-3;
FIG. 3 is a velocity trace diagram of agents 0-3;
FIG. 4 is a graph of acceleration trajectories for agents 0-3;
FIG. 5 is a communication time distribution of agent 1-2;
Fig. 6 is a schematic diagram of an electronic device according to an embodiment of the present invention.
Detailed Description
The following examples are only for more clearly illustrating the technical aspects of the present invention, and are not intended to limit the scope of the present invention. The present invention will be described in detail with reference to the accompanying drawings. The features of the examples and embodiments described below may be combined with each other without conflict.
The invention relates to an event triggering distributed optimal control system of an isomorphic multi-agent system, which comprises a distributed optimal control module and an event triggering consistency protocol module;
the event triggering consistency protocol module is used for giving event triggering conditions which can realize the consistency of a leader-following of the multi-agent system under an event triggering communication mechanism, and checking whether the event triggering conditions are met or not in each sampling period of the agent so as to determine the non-uniform communication moment of the agent;
And the distributed optimal control module is used for giving an analytical expression of the global optimal distributed control law under a periodic communication mechanism and a matrix equation set which needs to be met by a feedback matrix of the global optimal distributed control law based on the determined non-uniform communication moment of the intelligent agent by minimizing a secondary objective function and matrix decomposition about process state cost, control cost and state-control crossover cost, wherein the feedback control law can be implemented in a distributed manner and can enable global performance indexes to be optimal.
Specifically, the global optimal distributed control law is obtained through objective function weight matrix decomposition and submatrix equation set solution, and the intelligent agent of the isomorphic multi-intelligent agent systemIs expressed as:
(1);
The multi-agent system model is expressed as:
(2);
Wherein the method comprises the steps of In a multi-agent systemTime of dayA dimension state vector, superscript T, represents a transpose operation;, Is an intelligent body A kind of electronic deviceThe number of the intelligent agents in the multi-intelligent system is N+1; Is that A dimension control input is provided to the control system,Is an intelligent bodyA kind of electronic deviceA dimension control input is provided to the control system,AndRespectively of intelligent bodiesView system matrixA control matrix of dimensions is provided,Is thatThe dimensional identity matrix is used to determine the identity of the object,Represents the kronecker product;
the goal of optimal control of a multi-agent system is to minimize process state costs And control costAnd state-control cross costDefining an infinite time quadratic objective function of the isomorphic multi-agent system as:
(3);
Wherein the weight matrix Is thatA weight matrixIs thatMatrix of weightsIs thatIs a positive definite matrix of (2);
The global optimal control law for minimizing the secondary objective function can be obtained through the principle of maximum value:
(4);
positive definite matrix Is the only solution that satisfies the following matrix licarpa's equation:
(5);
If matrix ,,The method is divided into the following forms:
;;(6);
Design of submatrices The system of matrix equations is satisfied:
;;(7);
(8);
Wherein the method comprises the steps of As a result of the coupling coefficient,Laplacian matrix for multi-agent systems, i.e
;(9);
Wherein the method comprises the steps of,,Representing communication topology of a multi-agent system if agentsTo intelligent bodyThe sending state information is called as intelligent agentIs intelligentNeighbor and of (2)OtherwiseCollection ofTo intelligent bodyA set of neighbor agents;
The matrix licarpa's equation becomes:
(10);
Instant weight matrix The method meets the following conditions:
(11);
Global optimal distributed control law Distributed computing and implementation is possible, namely:
(12);
Wherein the method comprises the steps of For local feedback matrix, agentThe local feedback control law of (2) is expressed as:
(13);
wherein, Representing an agentNeighbor agent of (a)State of (2);
The closed loop multi-agent system model of local feedback is expressed as:
(14)。
In particular, leader-follower consistency of multi-agent systems through leader-follower communication topology and local feedback control
(15);
Wherein the method comprises the steps ofIs in the state of a leader and is an intelligent agentIs represented by a local feedback control law:
(16);
wherein, ,,Representing leader-follow communication topology if the leader is directed to an agentTransmitting status informationOtherwise;
When submatrixThe method meets the following conditions:
(17);
Wherein the matrix Sub-matrixSatisfying the matrix equation sets (8) and (11), the distributed control law is relatively quadratic objective functionIs optimal.
Specifically, calculating non-uniform communication time by using event-triggered communication conditions, constructing distributed event-triggered conditions and a threshold value of decay with time by using state estimation errors, and realizing leader-follower consistency of the multi-agent system;
Construction intelligent body Event trigger conditions of (2):
(18);
Wherein the state estimation error:
(19);
Wherein the method comprises the steps of Is an intelligent bodyState estimation value, threshold value of (2)As a decreasing function of decay to 0 over time, i.e. to satisfy
(20);
Checking event triggering conditions (18) at a set sampling frequency ifIf true, triggering the event, and recording the triggering time asWhen the agent isIs triggered by an event of (a) an agentTransmitting self state information to the neighbor agent, obtaining local feedback control law expression of agent j through formula (16), when agentWhen the event of (a) is not triggeredAnd does not send self state information to its neighbor agents.
Specifically, when the event of the intelligent agent is not triggered, the neighbor of the intelligent agent estimates the state of the intelligent agent by a closed-loop prediction method independent of real-time control informationIn cycles of the system model of (2)Performing first-order discretization to obtain:
21;
Intelligent body Neighbor agent of (a)Namely, receiving the agentStatus informationAccording to the agent of (2)At the current timeAnd the previous timeThe status information of (2) is obtained:
(22);
When the intelligent agent At the moment of triggeringDuring the time period that the post event is not triggered, the agentThe agent is estimated by the following equationState of (i.e. use of)For intelligent bodyPerforming closed-loop prediction of the state of (2);
(23);(24);
Wherein the method comprises the steps of Is a positive integer which is used for the preparation of the high-voltage power supply,Is an intelligent bodyIs the first of (2)Triggering time;
When the intelligent agent When the event of (a) is not triggered, its neighbor agentThe control law of (2) is:
(25)
wherein the aggregate Based on intelligent agentsIs a set of neighbor and triggered agents,Based on intelligent agentsIs a neighbor and the event does not trigger the set of agents,Is the state of agent l.
Specifically, the implementation steps are as follows:
Step1 initializing an agent model matrix 、Number ofWeight matrix of objective function、、And initial stateGiven a constantDetermining Laplacian matrix according to multi-agent communication network topology structure as sampling period;
Step 2 solving through the matrix equation sets (7) (8) (11)Obtaining a feedback matrix;
Step 3, circularly executing the following steps until:
Second to multiple agent systemThe intelligent agent is used for controlling the intelligent agent,Accepting neighbor state information,;
Neighbor agents that estimate non-transmitted state informationState of (2),;
Calculation (13) and (25) to obtain a distributed control lawAnd;
Checking event triggering conditions (18), and if the conditions are satisfied, transmitting status information to the neighborsAnd if the condition is not satisfied, not transmitting.
The invention also provides an event-triggered distributed optimal control method of the isomorphic multi-agent system, which comprises the following steps:
Giving event triggering conditions capable of realizing the consistence of a leader-follow of a multi-agent system under an event triggering communication mechanism, and checking whether the event triggering conditions are met or not in each sampling period of an agent so as to determine non-uniform communication time of the agent;
Based on the determined non-uniform communication time of the intelligent agent, by minimizing a secondary objective function and matrix decomposition about process state cost, control cost and state-control crossover cost, an analytical expression of a globally optimal distributed control law under a periodic communication mechanism is given, and a matrix equation set which needs to be satisfied by a feedback matrix of the globally optimal distributed control law is given, wherein the feedback control law can be implemented in a distributed manner and can enable global performance indexes to be optimal.
It should be noted that, the method embodiment shown in the present embodiment is matched with the content of the system embodiment, and reference may be made to the content of the system embodiment, which is not described herein.
The present invention will be described in detail with reference to the accompanying drawings.
A multi-agent system, as shown in fig. 1, comprises 4 homogeneous agents, each of which has the following model:
,;
the initial conditions are:
,,, the three states of the intelligent agent 0-3 are position, speed and acceleration respectively;
the communication topology of the multi-agent system is shown in fig. 1:
,;
Selecting: ,, it is possible to calculate:
,,
Selecting: Sampling period: Agent 0 is the leader, continuously sending status information to agent 1, and agents 1 and 2 intermittently send their own status information to their neighbor agents 2 and 3. The state trajectories of the agents 0-3 are shown in fig. 2-4, and the communication moments are shown in fig. 5. The triggering times of the intelligent agent 1-2 are respectively 12 times and 17 times, and the communication times can be reduced by more than 80% by adopting event triggering and closed-loop prediction relative to 80 communication moments sampled periodically.
The invention also provides electronic equipment, as shown in fig. 6, comprising a memory and a processor, wherein the memory is coupled with the processor, the memory is used for storing program data, and the processor is used for executing the program data to realize the event-triggered distributed optimal control method of the isomorphic multi-agent system.
It should be noted that, in addition to the memory and the processor shown in fig. 6, the electronic device may further include other hardware according to its actual functions, which will not be described herein.
The invention also provides a computer readable storage medium, on which a computer program is stored, which when executed by a processor implements an event-triggered distributed optimal control method of an isomorphic multi-agent system as described above.
The invention also provides a computer program product, which comprises a computer program, wherein the computer program realizes the event-triggered distributed optimal control method of the isomorphic multi-agent system when being executed by a processor.
It will be appreciated by those skilled in the art that embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
The above embodiments are merely for illustrating the design concept and features of the present invention, and are intended to enable those skilled in the art to understand the content of the present invention and implement the same, the scope of the present invention is not limited to the above embodiments. Therefore, all equivalent changes or modifications according to the principles and design ideas of the present invention are within the scope of the present invention.
Claims (9)
1. The event triggering distributed optimal control system of the isomorphic multi-agent system is characterized by comprising a distributed optimal control module and an event triggering consistency protocol module;
the event triggering consistency protocol module is used for giving event triggering conditions which can realize the consistency of a leader-following of the multi-agent system under an event triggering communication mechanism, and checking whether the event triggering conditions are met or not in each sampling period of the agent so as to determine the non-uniform communication moment of the agent;
The distributed optimal control module is used for giving out an analytical expression of a global optimal distributed control law under a periodic communication mechanism and a matrix equation set which needs to be met by a feedback matrix of the global optimal distributed control law based on the determined non-uniform communication moment of the intelligent agent by minimizing a secondary objective function and matrix decomposition about process state cost, control cost and state-control crossover cost, wherein the feedback control law can be implemented in a distributed manner and can optimize global performance indexes, and comprises the following steps:
Obtaining a global optimal distributed control law through objective function weight matrix decomposition and submatrix equation set solution, wherein the intelligent agents of the isomorphic multi-intelligent system Is expressed as:
(1);
The multi-agent system model is expressed as:
(2);
Wherein the method comprises the steps of In a multi-agent systemTime of dayA dimension state vector, superscript T, represents a transpose operation;, Is an intelligent body A kind of electronic deviceThe number of the intelligent agents in the multi-intelligent system is N+1; Is that A dimension control input is provided to the control system,Is an intelligent bodyA kind of electronic deviceA dimension control input is provided to the control system,AndRespectively of intelligent bodiesView system matrixA control matrix of dimensions is provided,Is thatThe dimensional identity matrix is used to determine the identity of the object,Represents the kronecker product;
the goal of optimal control of a multi-agent system is to minimize process state costs And control costAnd state-control cross costDefining an infinite time quadratic objective function of the isomorphic multi-agent system as:
(3);
Wherein the weight matrix Is thatA weight matrixIs thatMatrix of weightsIs thatIs a positive definite matrix of (2);
The global optimal control law for minimizing the secondary objective function can be obtained through the principle of maximum value:
(4);
positive definite matrix Is the only solution that satisfies the following matrix licarpa's equation:
(5);
If matrix ,,The method is divided into the following forms:
;;(6);
Design of submatrices The system of matrix equations is satisfied:
;;(7);
(8);
Wherein the method comprises the steps of As a result of the coupling coefficient,Laplacian matrix for multi-agent systems, i.e
;(9);
Wherein the method comprises the steps of,,Representing communication topology of a multi-agent system if agentsTo intelligent bodyThe sending state information is called as intelligent agentIs intelligentNeighbor and of (2)OtherwiseCollection ofTo intelligent bodyA set of neighbor agents;
The matrix licarpa's equation becomes:
(10);
Instant weight matrix The method meets the following conditions:
(11);
Global optimal distributed control law Distributed computing and implementation is possible, namely:
(12);
Wherein the method comprises the steps of For local feedback matrix, agentThe local feedback control law of (2) is expressed as:
(13);
wherein, Representing an agentNeighbor agent of (a)State of (2);
The closed loop multi-agent system model of local feedback is expressed as:
(14)。
2. The event-triggered distributed optimal control system for a homogeneous multi-agent system of claim 1, wherein a leader-follower consistency of the multi-agent system is achieved through a leader-follower communication topology and local feedback control
(15);
Wherein the method comprises the steps ofIs in the state of a leader and is an intelligent agentIs represented by a local feedback control law:
(16);
wherein, ,,Representing leader-follow communication topology if the leader is directed to an agentTransmitting status informationOtherwise;
When submatrixThe method meets the following conditions:
(17);
Wherein the matrix Sub-matrixSatisfying the matrix equation sets (8) and (11), the distributed control law is relatively quadratic objective functionIs optimal.
3. The event-triggered distributed optimal control system of a homogeneous multi-agent system of claim 2, wherein non-uniform communication time is calculated by event-triggered communication conditions, distributed event-triggered conditions and thresholds for decay over time are constructed by state estimation errors, and leader-follower consistency of the multi-agent system is achieved;
Construction intelligent body Event trigger conditions of (2):
(18);
Wherein the state estimation error:
(19);
Wherein the method comprises the steps of Is an intelligent bodyState estimation value, threshold value of (2)As a decreasing function of decay to 0 over time, i.e. to satisfy
(20);
Checking event triggering conditions (18) at a set sampling frequency ifIf true, triggering the event, and recording the triggering time asWhen the agent isIs triggered by an event of (a) an agentTransmitting self state information to the neighbor agent, obtaining local feedback control law expression of agent j through formula (16), when agentWhen the event of (a) is not triggeredAnd does not send self state information to its neighbor agents.
4. The event-triggered distributed optimal control system of a homogeneous multi-agent system of claim 3, wherein when an agent's event is not triggered, an agent's neighbors estimate the agent's state by a closed-loop prediction method independent of real-time control informationIn cycles of the system model of (2)Performing first-order discretization to obtain:
21;
Intelligent body Neighbor agent of (a)Namely, receiving the agentStatus informationAccording to the agent of (2)At the current timeAnd the previous timeThe status information of (2) is obtained:
(22);
When the intelligent agent At the moment of triggeringDuring the time period that the post event is not triggered, the agentThe agent is estimated by the following equationState of (i.e. use of)For intelligent bodyPerforming closed-loop prediction of the state of (2);
(23);(24);
Wherein the method comprises the steps of Is a positive integer which is used for the preparation of the high-voltage power supply,Is an intelligent bodyIs the first of (2)Triggering time;
When the intelligent agent When the event of (a) is not triggered, its neighbor agentThe control law of (2) is:
(25)
wherein the aggregate Based on intelligent agentsIs a set of neighbor and triggered agents,Based on intelligent agentsIs a neighbor and the event does not trigger the set of agents,Is the state of agent l.
5. The event triggered distributed optimal control system of a homogeneous multi-agent system of claim 4, comprising the steps of:
Step1 initializing an agent model matrix 、Number ofWeight matrix of objective function、、And initial stateGiven a constantDetermining Laplacian matrix according to multi-agent communication network topology structure as sampling period;
Step 2 solving through the matrix equation sets (7) (8) (11)Obtaining a feedback matrix;
Step 3, circularly executing the following steps until:
Second to multiple agent systemThe intelligent agent is used for controlling the intelligent agent,Accepting neighbor state information,;
Neighbor agents that estimate non-transmitted state informationState of (2),;
Calculation (13) and (25) to obtain a distributed control lawAnd;
Checking event triggering conditions (18), and if the conditions are satisfied, transmitting status information to the neighborsAnd if the condition is not satisfied, not transmitting.
6. An event-triggered distributed optimal control method for an isomorphic multi-agent system, comprising the steps of:
Giving event triggering conditions capable of realizing the consistence of a leader-follow of a multi-agent system under an event triggering communication mechanism, and checking whether the event triggering conditions are met or not in each sampling period of an agent so as to determine non-uniform communication time of the agent;
Based on the determined non-uniform communication time of the agent, by minimizing a secondary objective function and matrix decomposition about process state cost, control cost and state-control crossover cost, an analytical expression of a globally optimal distributed control law under a periodic communication mechanism is given, and a matrix equation set to be satisfied by a feedback matrix of the globally optimal distributed control law is given, where the feedback control law can be implemented in a distributed manner and enables global performance indexes to reach an optimal level, including:
Obtaining a global optimal distributed control law through objective function weight matrix decomposition and submatrix equation set solution, wherein the intelligent agents of the isomorphic multi-intelligent system Is expressed as:
(1);
The multi-agent system model is expressed as:
(2);
Wherein the method comprises the steps of In a multi-agent systemTime of dayA dimension state vector, superscript T, represents a transpose operation;, Is an intelligent body A kind of electronic deviceThe number of the intelligent agents in the multi-intelligent system is N+1; Is that A dimension control input is provided to the control system,Is an intelligent bodyA kind of electronic deviceA dimension control input is provided to the control system,AndRespectively of intelligent bodiesView system matrixA control matrix of dimensions is provided,Is thatThe dimensional identity matrix is used to determine the identity of the object,Represents the kronecker product;
the goal of optimal control of a multi-agent system is to minimize process state costs And control costAnd state-control cross costDefining an infinite time quadratic objective function of the isomorphic multi-agent system as:
(3);
Wherein the weight matrix Is thatA weight matrixIs thatMatrix of weightsIs thatIs a positive definite matrix of (2);
The global optimal control law for minimizing the secondary objective function can be obtained through the principle of maximum value:
(4);
positive definite matrix Is the only solution that satisfies the following matrix licarpa's equation:
(5);
If matrix ,,The method is divided into the following forms:
;;(6);
Design of submatrices The system of matrix equations is satisfied:
;;(7);
(8);
Wherein the method comprises the steps of As a result of the coupling coefficient,Laplacian matrix for multi-agent systems, i.e
;(9);
Wherein the method comprises the steps of,,Representing communication topology of a multi-agent system if agentsTo intelligent bodyThe sending state information is called as intelligent agentIs intelligentNeighbor and of (2)OtherwiseCollection ofTo intelligent bodyA set of neighbor agents;
The matrix licarpa's equation becomes:
(10);
Instant weight matrix The method meets the following conditions:
(11);
Global optimal distributed control law Distributed computing and implementation is possible, namely:
(12);
Wherein the method comprises the steps of For local feedback matrix, agentThe local feedback control law of (2) is expressed as:
(13);
wherein, Representing an agentNeighbor agent of (a)State of (2);
The closed loop multi-agent system model of local feedback is expressed as:
(14)。
7. An electronic device comprising a memory and a processor, wherein the memory is coupled to the processor, wherein the memory is configured to store program data, and wherein the processor is configured to execute the program data to implement the event triggered distributed optimal control method of a homogeneous multi-agent system of claim 6.
8. A computer readable storage medium having stored thereon a computer program, wherein the program when executed by a processor implements an event triggered distributed optimal control method for a homogeneous multi-agent system as claimed in claim 6.
9. A computer program product comprising a computer program which, when executed by a processor, implements an event triggered distributed optimum control method for a homogeneous multi-agent system as claimed in any one of claims 6.
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