Optimal Design Of Formation Control Algorithms For Multi-agent Systems

As an important research direction of cooperative control of multi-agent systems,formation control has a wide application prospect in military,aerospace and industrial fields.It has been widely concerned by researchers from the fields of computer,control and artificial intelligence.The core problem of formation control is how to design distributed control protocol so that agents can achieve desired formation through local information interaction.Most of the current research focuses on how to design controllers to achieve formation,while paying less attention to the convergence rate of formation.However,in practical applications,not only formation needs to be achieved,but also important indicators such as the time when the formation is achieved or convergence rate need to be considered.For discrete systems,the conditions for achieving formation are easy to obtain,but the analytical solution method for optimal control protocol is still a difficult point.This paper uses the consensus protocol optimization design method,combined with memory acceleration idea,studies the optimal design problem of formation control algorithm for multi-agent system,aiming at finding the optimal control gain and optimal convergence rate of system,making system achieve formation fastest.In addition,this paper also considers whether system has leader or not.For the system without leader,the leader’s velocity is constant,and the leader’s velocity is time varying,the optimal designs of the control algorithms are given respectively.The main research contents of this paper are as follows:(1)Aiming at the formation control problem of second-order discrete multi-agent systems,the method of node memory acceleration is extended to formation control.A formation control protocol with velocity memory is designed,and the optimal control gain and convergence rate are given to make the system achieve formation fastest.Compared with the existing formation control protocol without velocity memory,the acceleration effect of velocity memory is analyzed.(2)Aiming at the leader-following formation control problem for first-order discrete multi-agent systems,the case where the leader moves at a constant velocity is considered,and a formation control protocol with integrator is designed.The sufficient conditions for the system to achieve the leader-following formation are given by the Jury criterion.By converting the fast formation problem into an optimal design problem of matrix spectral radius,an explicit formula is obtained for the optimal control gain of the system to achieve the fastest leader-following formation.(3)Aiming at the formation control problem of second-order multi-agent systems with a virtual leader of time-varying velocity,a distributed control protocol is designed,which enables the system to track the time-varying reference velocity while achieving formation.For the two cases with or without relative velocity measurement,the optimal control gain and convergence rate of the system to achieve formation fastest are given respectively.The influence of relative velocity measurement on formation speed is studied.