Research On Controllability And Observability Of A Class Of Multi-agent Systems

Controllability and observability,as a basic problem of multi-agent system,is an important research topic of multi-agent system modeling,analysis and coordinated control.This paper combines the two to study.In multi-agent systems,fixed and switch behaviors exist widely.In this paper,we mainly use formation control,intelligent control,control theory,matrix analysis,graph theory,and MATLAB to study the controllability and observability of multi-agent systems under fixed topology and switching topology,respectively.The main research contents and conclusions are as follows:1.The controllability and observability of the leader-based multi-agent system in the first,second and high order integrators are studied.Based on the protocol,the algebra and graph feature judgment of controllability and observability of the first-order multi-agent system are established.In addition,the controllability and observability conditions of the second-order integrator and the higher-order integrator systems are obtained under the same leader-follower framework and a predetermined topology.At the same time,by analyzing the eigenvector of Laplacian matrix,the necessary and sufficient conditions for the controllability(observability)of the system are obtained.Finally,numerical examples and simulation are used to verify the accuracy of the theoretical results.2.The controllability and observability of discrete-time multi-agent system with switching topology are analyzed.For the second-order multi-agent system,firstly,the motion state of discrete-time linear system under switching topology is derived.Based on the observable state set and observable matrix,the sufficient and necessary conditions for the system to be controllable(observable)are obtained when the position information topology and the speed information topology are different and switched.Secondly,if both the location information topology and the velocityinformation topology are fixed,the system will change from the switching topology to the fixed topology.For the case of fixed topology,we get a necessary and sufficient conclusion.It is proved that the system is observable if and only if each subspace contains only zero vectors.Finally,the reliability of the theoretical results is verified by numerical examples and simulation.