Research On Formation And Containment Control Problems Of Multi-Agent Systems

With the interdisciplinary development of computer science,control science,biology,physical science,statistics,sociology,and the widespread application of multi-agent system in the flocking of multiple robot,formation control of unmanned aerial vehicle,attitude control of spacecraft,more and more attention has been paid to the distributed coordinated control of multi-agent systems.The formation and containment control analysis and controller design problems of multi-agent systems are investigated in this paper,and the limit of sensor communication range,the disturbance of the complicated unknown environment,the restriction of cost,the requirements of multi-task and high convergence rate are considered.The corresponding control protocols are designed to achieve the distributed coordinated control,including formation tracking,multi-formation,formation-containment and so on.The main work is as follows.For the actual demand of convergence time in the formation control of multi-agent systems,a finite-time control protocol is designed via the fast terminal sliding mode control method,and the finite-time formation tracking problem is studied under the control input of the leader is equal to zero or not,and a sufficient condition for achieving the finite-time formation tracking is obtained.It turned out that under the proposed protocol,all the followers can reach an expected formation in the finite time and the geometric center of all the followers can also track the leader's trajectory in the finite time.For the multi-formation control problem of multi-agent systems,a nonlinear leader-following model is considered,and a distributed multi-formation control protocol is proposed.Based on the algebraic graph theory and Lyapunov stability theory,the multi-formation control for multi-agent systems is achieved,and a sufficient condition for reaching and maintaining multi-formation control is given.For the containment control problem of the multi-agent systems with static and dynamic leaders,two control protocols are designed.Leaders are static,a protocol with control gain coefficient is proposed,while leaders are dynamic,a protocol based on sampling position data is proposed for the discrete multi-agent systems.With the help of the related knowledge of the linear matrix inequality,algebraic graph theory and Lyapunov stability theory,the conditions for gain coefficient and sampling period are given to achieve static and dynamic containment control,respectively.For the containment control problem of multi-agent systems,taking the disturbance of the unknown environment into consideration,two cases that agent's information is available or not are discussed.If the agent's information is available,based on the disturbance observer and relative state information of the neighbors,a state feedback control protocol is proposed.If the agent's information is not available,an output feedback control protocol is designed by the disturbance observer and state observer.By using the tools from the linear matrix inequality,feedback control theory and Lyapunov stability theory,sufficient conditions for reaching the state feedback containment control and output feedback containment control are obtained for the multi-agent systems with exogenous disturbance system.Considering the fact that leaders should interact with each other in order to perform complex tasks,the containment control problem of multi-agent systems with the leader's cluster dynamic behaviors is researched.Two formation containment control protocols are proposed under the fixed topology and switching topology,respectively,and the formation containment control for multi-agent systems is realized,that is,the states of leaders converge to an expected formation,while the states of all the followers converge into the convex hull spanned by those of the leaders,and move with the same speed as leaders.