Research On Optimal Control Of Linear Multi-agent Systems With Time-delay

In industrial production,generally the operation of equipment can not reach the ideal state,and the delay phenomenon is one of the problems that can not be avoided in the control process.The optimal control of time-delay systems has high research value and practical significance,and it is also one of the hot and difficult topics in recent years.As the basis of collaborative control between multiple agents,consensus issues attract increasing attention from researchers.In a multi-agent system,consensus means that the agents tend to be the same for some state,and the consensus algorithm is a protocol in which multiple agents are based on local information to make the individual state consistent.This paper focuses on consensus and control problem of the linear multi-agent systems with time-delay.The main contents and research results of this paper are summarized as follows:1.We studied weighted average consensus problem of linear multi-agents with time-varying delay.By integrating the weighted average coefficients into the controller parameter design,the synthesis of multi-agent systems is greatly facilitated.Based on algebraic graph theory and matrix analysis tool,we studied the weighted average consensus of multi-agents with time-varying delay and fixed topology and switching topologies respectly.We utilize the Lyapunov-Krasovskii theory to give the sufficient conditions for the linear control protocol achieving weighted average consensus in the form of LMI.The conclusion proves that all the nodes reach the weighted average of the initial state of the agents when they are stable.2.We studied consensus problem of the discrete-time multi-agents systems with time-delay.Based on the Lyapunov stability theorem,by constructing the Lyapunov functional and preserving the useful information in the Lyapunov functional difference,a sufficient condition for the stability of the system is given by using the linear matrix inequality method.And the set of matrix solutions satisfying the time delay range and the stability condition of the system can be obtained by the example calculation,which verifies the validity and feasibility of the conclusions obtained in this paper.3.The optimal control problem for linear multi-agent systems with time-delay is considered.Firstly,for the optimal state adjustment problem of systems with time-delay,a special solution is obtained for the state equation with time-delay and according to the properties of Cauchy's formula.The state feedback control law of the linear closed loop system is given and the solution of the optimal controller is obtained.Secondly,for the optimal tracking problem of multi-agents systems with time-delay in finite time domain,a linear system with input time-delay is transformed into a system without time-delay.Riccati matrix equations are constructed according to the optimal control theory,and a dynamic output feedback optimal tracking control algorithm is proposed.Finally,we verified the correctness and validity of the conclusion in this paper by computer simulation.