Iterative Learning Control For A Class Of Multi-agent Systems With Variable Interval Length

As an important branch of distributed artificial intelligence,multi-agent systems can transform large and complex systems into small ones that communicate with each other and are easy to manage.In recent years,the multi-agent system has been widely used in many practical engineering fields and has attracted great attention from domestic and foreign experts and scholars in the field of control.In the coordination and cooperative control of multi-agent systems,consensus has become a hot spot as a fundamental issue.Iterative learning control has been widely used in the research of multi-agent systems with repetitive operation because it can accurately track the desired trajectory in a fixed time interval.However,in the actual system learning process,due to the influence of complex conditions,the system may be interrupted at any time during the repeated operation,so that each iteration learning process may be interrupted,and thus can not reach the identical length as the desired trajectory interval,thus limiting the application of iterative learning control algorithm.In this case,aiming at a kind of multi-agent system that performs repetitive control tasks,this paper studies the desired trajectory tracking and formation control effect of the algorithm under the condition of variable interval length.The main work of this paper is divided into the following sections:(1)The problem of consensus for linear discrete multi-agent system with leader agent is considered.It is assumed that the communication topology of the multi-agent system is fixed.The variation of the length of the learning interval is described by a certain probability distribution.Due to the random variation of the iterative learning interval length,the length of the output data of the system also varies randomly.A distributed P-type iterative learning control algorithm is proposed based on the improved consensus error.The sufficient condition of the system convergence is given.By using the method of contraction mapping,it is proved by strict theoretical derivation that the proposed algorithm can fully track the desired trajectory in the case of initial state error.Finally,the MATLAB simulation verifies the effectiveness of the algorithm.(2)The problem of consensus for nonlinear discrete multi-agent system withleader agent is considered.It is assumed that only a part of the agents in the multi-agent system can obtain the leader information under the communication topology.In the case of random variation of iterative learning interval length,the iterative learning control algorithm is designed using only partial tracking error,and the sufficient condition for the system to achieve complete agreement is given.The convergence of the algorithm is proved by strict theoretical derivation.Finally,the MATLAB simulation verifies the effectiveness of the algorithm.(3)The formation control problem of linear discrete multi-agent system with leader agent is considered.It is assumed that the multi-agent system has fixed communication topology,and the follower agent and the leader agent maintain a fixed formation form motion.According to the topology connection structure of the agent,the formation control problem can be transformed into the tracking problem.Under the conditions that the variable iterative learning interval length and the initial state deviation,the consensus error of multi-agent system is constructed,and the convergence of the system in norm sense is analyzed based on the contraction mapping method.Finally,the MATLAB simulation verifies the effectiveness of the algorithm.