Research On Consensus Of Multi-agent System By Iterative Learning Control

Multi-agent system refers to a type of complex networked system that is composed of multiple self-agents and completes tasks through partial interaction that cannot be completed by a single agent.It's research results are important theoretical foundations in the fields of multi-robot collaborative control,smart grid,smart transportation,and distributed computing.Among them,the consensus problem is the core problem in the research of multi-agent systems.This paper uses iterative learning control methods to study the consensus of multi-agent system with limited measurement,disturbance,and multiple delays.The main contents are as follows:(1)Considering the situation of communication interference,corresponding iterative learning consensus algorithms are designed for a class of time-varying linear systems and a class of time-varying nonlinear systems with fixed topology,which can suppress any type of repeated interference.First,under the condition that the initial state can be reset to zero,a distributed control protocol based on iterative learning is designed for the time-varying linear multi-agent system according to the local information that the agent can obtain.Then,the sufficient conditions for the solvable consensus problem of the system are obtained by the method of linear matrix inequality(LMI).Similarly,for a class of nonlinear time-varying multi-agent systems,an iterative learning control protocol is designed based on the local information that the agents can obtain,and sufficient conditions for the consensus problem to be solvable are given.The simulation results show that the proposed method can solve the corresponding consensus problem and realize the suppression of any type of disturbance.(2)The output consensus problem of the continuous linear multi-agent system based on the iterative learning control method is studied at the situation that the communication topology is switched along the time axis and iterative axis at the same time the measurement is limited,and then,two types of sufficient conditions for the problem to be solvable are obtained.Under the condition that the initial state of all agents can be reset in each iteration,the measurement restricted distributed control protocol is designed for the local information that the follower can obtained with the system communication topology always contains a spanning tree with the virtual leader as the root node.Two sufficient conditions for the output of all followers to converge to the output of the virtual leader are given,one of which can realize the distributed calculation of time-varying iterative learning gain.The simulation results show that the proposed method is effective.(3)In view of the limited measurement and the communication topology switching along the time axis and the iterative axis and the conditions of united unicom are met,the output consensus problem of the continuous nonlinear multi-agent system is studied by iterative learning,and two sufficient conditions for the problem to be solvable are obtained.Under the condition that the initial state of all agents can be reset in each iteration,a measurement constrained output consensus protocol is designed based on local information,and the sufficiency condition of the system's solvable consensus problem is given using the LMI method.On this basis,the unknown parameters in the obtained sufficiency conditions are maximized,and the second sufficiency condition is given by combining Gersgorin's disc theorem and LMI method,which makes the design of learning gain easier and more feasible.The simulation results verify the effectiveness of the proposed algorithm.(4)In the case of both state and communication delay,the iterative learning consensus problem of a class of nonlinear multi-agent systems is explored with the communication topology is switching in both the time axis and the iteration axis,and sufficient conditions for the problem to be solvable are obtained.In particular,the input coefficient in the system is a nonlinear function with multiple state delays,so there is a mixed term between multiple state delays and communication delays.According to the local information that the individual agent can obtain,and based on the iterative learning control method,a distributed algorithm controller with undetermined gain is established.After that,the sufficient conditions for reaching consensus are obtained by using the analysis method of linear inequality.Finally,the simulation experiment results show the practicability and effectiveness of the theory in this paper.