The Containment Control Problem Of Nonlinear Multi-agent Systems With Time Delays

Containment control is one of the important problem in cooperative control of multi-agent systems.In a multi-agent system with multiple leaders,some control strategies need to be designed to steer followers approaching or entering the convex hull spanned by leaders,which is the main purpose of containment control.Many nature phenomena and engineering applications are related to containment control(such as UAV flocks),so the containment control problem is getting more and more attention in recent years.In existing literature,the research on containment control is mainly for linear multi-agent system and time-delays are mostly fixed.However,the systems are mostly nonlinear with time-varying delays in real world.Consequently,it is of great theoretical and practical value to consider the containment control problem based on nonlinear and time-varying delayed model.Furthermore,in order to save communication resources,we introduce event-triggered control strategies,and consider switched,noise,disturbance phenomena,on this basis,we derive some sufficient conditions to ensure that each follower ultimately enters the neighbourhood of the convex hull spanned by leaders,thus generalizing the existing result.The study contents are as follows:In the first chapter,the research background and research situation on containment control problem are described,then the main research contents and innovation points are given.In the second chapter,the containment control problem of nonlinear discrete system based on dynamic event-triggered strategy is studied.The multi-agent system includes followers and leaders.The local dynamical system under consideration is nonlinear and with time-varying delays.The containment control agreement is an interaction between the followers and leaders,and the dynamic event-triggered control is realized by introducing an internal dynamical variable.Under a certain assumption on the connectivity of the whole network,by constructing Lyapunov functional,and using some mathematical analytical techniques,the sufficient conditions on LMIs are derived to ensure that each follower ultimately enters the neighbourhood of the convex hull spanned by leaders,the numerical example finally validates the results.In the third chapter,the containment control problem of nonlinear continous system with switched topology and white Gaussian noise is studied.The system consists of discrete and distributed time-varying delays.The proposed protocol is characterized by time-varying delays and switched topology.By constructing mode-dependent Lyapunov-Krasovskii functional,and using average dwell time method,stochastic analysis,some new analytical techniques,the sufficient conditions are derived to ensure that each follower converges to the convex hull spanned by leaders in mean square.A numerical example validates the effectiveness of the results.In the forth chapter,the containment control problem of nonlinear continous system with unknown disturbance is considered.The system consists of distributed time-varying delays.The protocol based on event-triggered strategy is used to save cost.The system is converted into an error system by a variable substitution,thus transforming the containment control problem into the ultimate bounded problem of the solution to the error system.By an assumption that the unknown disturbances of agents are norm bounded,and by constructing suitable Lyapunov functional,sufficient conditions are derived to ensure that the each follower enters the neighbourhood of the convex hull spanned by leaders.In addition,the Zeno behaviour is excluded.A numerical example validates the effectiveness of the results.