Research On Event-Triggered Sampled-Data Control For Linear Multi-Agent Systems

This thesis studies event-triggered coordinated control problems of linear multi-agent systems,including consensus problems,distributed optimization problems,noncooperative game problems and multi-cluster noncooperative game problems.The new event-triggering sampling method enables systems to sample intermittently according to their real-time states.The remarkable advantages of event-triggering sampling in saving communication resources make it gradually become a research hotspot in multi-agent systems.At present,there are still many problems to be solved in the research of eventtriggered control in multi-agent systems.This thesis focuses on the event-triggered coordinated control problems of multi-agent systems where agents follow complex dynamics,and designs new distributed control protocols and event-triggering mechanisms.The specific research work of this thesis is as follows:(1)Distributed optimization problems of dynamic event-triggered control for heterogeneous linear multi-agent systems in digraphs are studied.In order to reduce the cost of communications among agents,event-triggering mechanisms are used to determine the instants of sampling.The designed thresholds of event triggering condition depend on dynamic variables,exponential decay function and sampled values of decision variables.The introduction of non-negative dynamic variables can increase the inter-event times.Using Lyapunov stability theorem,convex optimization theory and other related results,the convergence of decision variables is systematically analyzed,and the minimum interevent time is given by calculation.The positiveness of the minimum inter-event time can avoid the Zeno phenomenon.The simulation results show that the dynamic eventtriggerring conditions designed in this thesis can further reduce sampling frequencies.(2)Noncooperative game problems of time-event-triggered control for heterogeneous linear multi-agent systems are studied.First,in the case of the games with the incomplete information,distributed Nash equilibrium seeking protocols based on discrete-time information are proposed.Secondly,the time-event-triggering sampling is designed based on periodic sampling and event-triggered sampling,and has the advantages of both periodic sampling and event-triggered sampling.After each event,it starts to judge whether the measurement error exceeds the designed threshold.This detection method directly avoids the Zeno phenomenon.The threshold in the event-triggering condition depends on a dynamic variable and an exponential decay function,and the decay threshold does not affect the convergence of strategies.Finally,using game theory,matrix theory and other related results,the sufficient conditions for the strategies of players to converge to a Nash equilibrium are given.(3)Multi-cluster noncooperative game problems in heterogeneous linear multi-agent systems based on two event-triggering conditions are studied.New Nash equilibrium seeking protocols and event-triggering mechanisms are designed.The novelty lies in providing a theoretical framework for the design and analysis of event-triggered control protocols in heterogeneous linear multi-agent systems.The multi-cluster noncooperative game problems include consensus problems,distributed optimization problems and non cooperative game problems.Another novelty is that the event-triggering mechanisms includes periodic sampling mechanisms,event-triggering mechanisms with constant thresholds,event-triggering mechanisms with exponential decay thresholds and dynamic event-triggering mechanisms.This new event-triggering mechanisms can reduce the cost of communications among agents.The design of thresholds does not rely on any decision variables,and can avoid the Zeno phenomenon.It does not affect the convergence of decision variables.Based on convex optimization theory,game theory,matrix theory and other related results,sufficient conditions are given to ensure that the decision variables converge to the Nash equilibrium,and the minimum inter-event time is given.(4)The consensus of event-triggered control for linear multi-agent systems with two event-triggering mechanisms is studied.In order to reduce the costs of communications among agents and the communications of control signals from controllers to actuators,each agent is equipped with two event-triggering mechanisms.We have considered the two cases that the two event-triggering mechanisms are time-event-triggering mechanisms or event-triggering mechanisms based on two event-triggering conditions.In the two cases,the minimum inter-event time is positive,which avoids the Zeno phenomenon.Because of the coupling between the two event-triggering mechanisms,the parameters of two eventtriggering mechanism parameters are coupling.In this case,in order to ensure the consensus of states,Lyapunov stability theorem is used to give the constraint conditions that event-triggering condition parameters satisfy.