Research On Several Types Of Formation Control Problems Of Multi-agent Systems

With the rapid development of information technology and the wide application of networked systems in computer science,smart grid,spacecraft,mobile robots,sensor networks and other fields,the problem of distributed cooperative control of multi-agent systems has attracted the attention of many scholars.Due to the practical application of formation behavior of agents in many scenarios such as military reconnaissance,target tracking and disaster detection,formation control has become one of the most active research topics in the control of multi-agent systems.In consideration of the various types of formation tasks and performance constraints encountered in practical application scenarios,cluster formation and bipartite formation are discussed in this paper,and the guaranteed performance and optimal control problems are also discussed.For nonlinear or uncertain multi-agent systems,event-triggered sampling,impulse and data-driven formation control protocols are designed to reduce communication pressure and energy consumption.Specifically,the main works of this thesis are as follows.(1)To solve the problem of cluster formation and its performance constraints under the action of hybrid impulses,firstly,two state feedback control protocols are proposed based on global and local information interaction respectively;Then,the definition of average impulse gain and average impulse interval is introduced,and the corresponding clustering formation conditions are established by using algebraic graph theory and Lyapunov stability theory;In view of the performance constraints related to the velocity of agents,a global performance index function is defined.Sufficient conditions to realize guaranteed-performance cluster formation of multi-agent systems are given and the upper bound of the performance index is also obtained.(2)For the optimal cluster formation of multi-agent systems with completely unknown system dynamics,data-driven adaptive dynamic programming method is used to design the control strategy.Firstly,a definition of performance index containing clustering formation error and control input is given.Based on the Bellman optimality principle,the optimal clustering formation problem is constructed and the optimal controller based on the system model is obtained.In order to get the optimal control strategy when the system model is unknown,a data-driven strategy iteration algorithm based on -function is designed and implemented using actor-critic neural network framework.Meanwhile,the convergence of the strategy iteration algorithm and the stability of the error system are analyzed.(3)For multi-agent systems with antagonistic interactions,bipartite formation problem model is proposed.With the action of hybrid impulses,fixed and adaptive state feedback control protocols are established respectively.Firstly,the bipartite formation conditions of multi-agent systems under hybrid impulses are obtained by using the consensus strategy;Then,for the problem that the control gain in the fixed state feedback controller is difficult to be solved due to the unknown nonlinear term,an impulsive-adaptive control strategy is established.As long as the average impulse gain is less than 1,the adaptive control strategy can always guarantee the realization of bipartite formation.(4)To solve the problem of limited energy supply in bipartite formation control,event-triggered sampling control protocol is designed,and guaranteed-performance bipartite formation conditions are established.Firstly,the event conditions of the leader and followers are designed respectively,and the bipartite formation conditions based on LMI are established by using Lyapunov stability theory;Then,the performance index including bipartite formation error and control input is defined and the guaranteed bipartite formation conditions and the upper bound of the performance index are obtained,so that the system can meet the energy consumption constraint while achieving bipartite formation.(5)In order to solve the formation control problem of complex nonlinear systems,two sets of formation conditions based on fuzzy control system are established.Firstly,the T-S fuzzy model is used to approximate the nonlinear system,event-triggered sampling fuzzy controller is designed which does not have to match the fuzzy rules with the system;Then,by means of Lyapunov stability theory and matrix inequality technique,a set of formation conditions of fuzzy control system is established.In order to reduce the conservatism of formation conditions,by introducing the characteristics of membership function into formation analysis,formation conditions dependent on membership function(MFD)are obtained.