Impulsive Consensus Of Multi-agent Nonlinear Systems

In recent years,there has been an increasing interest in the research on multi-agent systems(MAS)due to its widespread applications in many fields,such as physics,science and mathematics.Most of the existing research on MAS is about continuous control,and there is not much research on impulse control.Many significant results have been developed for consensus and synchronization control of linear MAS.All these mentioned literatures are commonly devoted to investigate impulsive dynamical control systems without disturbances and uncertainties.Considering the nonlinear and uncertainties in multi-agent systems,two more practical multi-agent impulsive synchronization control algorithms are proposed.The main contents of this paper are considered as follows:(1)The problem for nonlinear multi-agent systems with stochastic disturbance is considered.For a multi-agent system with stochastic perturbation,not only the random perturbation part but also the nonlinear coupling relation is considered.The distributed impulsive synchronization control algorithm is designed by using the state error for the feedback control input.Based on the theory of impulsive differential system and the stability analysis of Lyapunov,the relationship between random perturbation and nonlinear coupling matrices is discussed,and the stability domain of control pulse interval is given.The proposed distributed pulse control algorithm only needs to obtain the neighbor state information and respond at the pulse time,which greatly reduces the control cost of the system.(2)The problem for nonlinear multi-agent systems with impulsive disturbance is considered.For the stochastic multi-agent system with impulsive disturbance,the state mutation of the impulse time is added as the pulse interference to the system analysis.Through the design of the distributed continuous control algorithm,the consistency control of the multi-agent system is realized.Considering the relationship between the control gain error and the impulse interference factor in the continuous control,the range of the interference frequency of the different communication topology and the coupling matrix is discussed based on the Lyapunov stability theory.(3)The problem for impulsive consensus of multi-agent nonlinear systems with control gain error is considered.For a nonlinear multi-agent system,consider the influence of the controller on the impulsive control time.Based on the analysis of the stability of Lyapunov theory,the relationship between control gain,control gain error and communication topological relation is analyzed.The stability of state synchronization error is analyzed theoretically,and then the communication topology is switched at the time of pulse control.The constraint condition of synchronization error stability under switching topology is discussed.