Research On Optimal Control Problem Of Multi-agent Systems With Time Delay

Multi-agent systems have a wide range of applications in related fields such as medical rescue,public safety,and environmental pollution,and the research on multi-agent systems has been a hot topic in recent years.Consensus problem is one of the most basic issues in the study of multi-agent systems.In the process of studying consensus,time delay will affect the performance and stability of the system,so time delay is an important factor that cannot be ignored.In addition,the cost,energy,and other issues should also be considered in the process of studying the consensus of multi-agent systems.Therefore,this article mainly studies the consensus and optimal control problem of multi-agent systems with state delay,and obtains the consensus and optimal control strategy of multi-agent systems by designing distributed reduced-order observers and controllers.The specific research work is as follows.(1)The consensus of the hysteresis multi-agent system with output feedback is studied by designing distributed reduced-order observers and controllers,which convert the consensus problem of the multi-agent system into a stability problem of the system.Then,the LyapunovKrasovskii functional is constructed,and the asymptotic stability of the transformed system is obtained by combining the properties of the matrix Kronecker product and the Schur complement theorem.The consensus of the multi-agent system is thus obtained,and the effectiveness of the theoretical results is demonstrated through Matlab programming simulation.(2)Using the 1-norm and ∞-norm of matrices,the consensus of the hysteresis multi-agent system is studied.Based on the observer with state delay and the output information of the neighboring intelligent agents,the controller is designed to obtain the asymptotic stability of the system.The effectiveness of the theoretical results is demonstrated through Matlab programming simulation.(3)The optimal control problem of the multi-agent system is studied.Firstly,the controllability of the error system is proved.Secondly,based on the quadratic performance index of the error system between the multi-agent systems given by practical applications,Hamilton function is constructed,and the optimal control strategy is obtained by the principle of dynamic programming.Then,the HJB equation is solved using reinforcement learning algorithm.Subsequently,the asymptotic stability and consensus of the system are proved by constructing Lyapunov functionals.Finally,the theoretical results are verified through example simulation.