Synchronization Control Of Fractional-order Nonlinear Systems With Impulsive Effect

In recent years,distributed collaborative control of fractional order nonlinear systems is wildly used in biological,physical and engineering systems,such as cluster problems and the formation of robotic systems.As a special class of multi-agent systems,the synchronization of chaotic system is an important research point of communication security engineering that attracted many researchers to carry out the research.Synchronization of multi-agent systems is also a very important and valuable fundamental study in distributed control area,which core goal is to select an appropriate control protocol that enables the state of all nodes in the network to be consistent.In the study of synchronization control of chaotic systems and multi-agent systems,impulsive control has become a very effective control method.In this paper,the main line of research is impulsive theory and synchronization control of fractional-order systems.The main works are given below.(1)For fractional-order nonlinear chaotic systems and multi-agent systems with impulsive disturbance,the suitable controller is designed by choosing the state error as the input signal,which is approved to realize the synchronization.Based on Caputo fractional derivative,Mittag-Leffler function and Lyapunov stability,sufficient control conditions are derived to ensure synchronization with impulsive disturbance.(2)The synchronization problem of fractional-order nonlinear chaotic systems and multi-agent systems when control gain error exists is mainly discussed.By analyzing the parameter conditions of controller,the distributed impulsive controller is designed,and impulsive interval and the stability domain of control gain are given.The impulsive controller only needs to receive the system state and respond at the pulse time,which greatly reduces the control cost.(3)The impulsive synchronization problem of fractional-order chaotic systems is investigated with actuator saturation.Based on the theory of fractional-order system and impulsive differential system and discontinuous Lyapunov stability,some sufficient conditions are given to guarantee the impulsive synchronization of typical nonlinear fractional-order chaotic systems.Then,the actuator saturation and control gain error are discussed simultaneously,which is more rigorous and practical in real systems.