Research On Formation-containment Control Of Multi-agent Systems Based On Fixed-time Convergence

With the development of communication technology,large-scale and high-efficiency communication has become possible,which makes the cooperative control of multi-agent systems researched and applied by many scholars,such as drone power inspection,multi-microgrid optimized control,and multi-robot systems control and so on.Under the conditions of communication constraints,the distributed multi-agent systems control protocol is designed to complete a variety of complex control tasks that a single agent cannot achieve.On the one hand,most of the existing research results are based on asymptotic convergence and finite-time convergence,that is,the entire control system can reach a stable state in an infinite or finite time,which is difficult to meet the needs of actual engineering problems.However multi-agent systems cooperative control based on fixed-time convergence can calculate the stable time of the entire system by using the designed control protocol parameters.On the other hand,most of the control problems in multi-agent cooperative control,such as consensus,formation control,containment control and so on,are single collective behavior,which is difficult to meet the requirements of diversified control tasks,while formation-containment control is multiple collective behaviors.And the above single collective behavior can be regarded as special cases of formation-containment control under certain conditions.Therefore,it has important theoretical and practical significance to study formation containment control based on fixed-time convergence.The main research contents of this paper are as follows:In the first part,the formation and consensus tracking control problems of multi-agent systems with second-order dynamics based on fixed-time convergence are studied.First,when the position state and velocity state of neighboring agents are available,the sliding mode control method is used to design a distributed control protocol based on fixed-time convergence,and the sufficient conditions for the multi-agent systems to achieve fixed-time convergence are given.Secondly,the results show that under the effect of the designed control protocol,within a time related to the control protocol parameters,the followers can form the designed formation,and the geometric center of the formation can follow the leader to move synchronously.Then,as a special case of formation control,a multi-agent systems consensus tracking control protocol based on fixed-time convergence is given as a corollary.Finally,some numerical simulation examples are given to verify the effectiveness of the designed control protocol.In the second part,formation-containment tracking control problems of multi-agent systems with second-order dynamics based on fixed-time convergence are studied.Firstly,based on the state information of neighboring agents,the error system is designed,and the sliding mode control method is used to design a distributed control protocol based on fixed-time convergence,and the sufficient conditions for the error system to achieve fixed-time convergence are given.Secondly,the results show that under the effect of the designed control protocol,within a fixed time,the sub-leader agents can form the designed formation,while the follower agents can converge to the geometric convex hull formed by sub-leader agents,and then all agents follow the main-leader synchronized movement.Then,some corollaries are put forward to solve other multi-agent cooperative control problems.Finally,numerical simulation examples are given to verify the effectiveness of the designed control protocol.