Research On Bipartite Consensus Of Nonlinear Multi-agent Systems And Time-varying Impulsive Control Of Chaotic Systems

There are many nonlinear systems in the field of control science.Many scholars pay attention to them because of their complex dynamic behaviors.There are two typical nonlinear systems:nonlinear multi-agent systems and chaotic systems,we study their stability and synchronization under different controllers in this thesis.A Multi-agent system is a kind of complex system coupled by many single agents.The cooperative control of multi-agent systems is widely used in manipulator operation,unmanned submarine operation,intelligent distribution and so on.Most scholars consider the consensus of multi-agent systems with only cooperative relationship.However,there is not only cooperative relationship but also competitive relationship in multi-agent systems.Therefore,it is more practical to consider the bipartite consensus of multi-agent systems with both cooperative and competitive couplings.Some nonlinear systems become chaotic systems under certain conditions.The stability control of chaotic systems is widely used in information encryption,image decryption,medical engineering and other fields.Many scholars consider the fixed time impulsive control of chaotic systems,but the impulse may occur at any time in the impulse-time window,so it is more general to study the time-varying impulsive control of chaotic systems.The main work of this thesis is as follows:The chapter 2 studies the problem of bipartite consensus of nonlinear multi-agent systems under stochastic switching topology.Firstly,considering the uncertain factors of the external environment,we introduce the transition probability into the switching rules.A multi-agent system model with cooperative and competitive couplings under stochastic switching topology is established,which has more practical significance.Secondly,in order to reduce control cost and update frequency,a novel event-triggered control protocol is designed.Some sufficient criteria for the bipartite consensus of the multi-agent systems are obtained by using Lyapunov functions and linear matrix inequality.Finally,a numerical example is given to verify the theoretical result.The chapter 3 investigates the stability and synchronization of chaotic systems under time-varying impulsive control.Firstly,the stability of a class of chaotic systems with impulse-time windows is discussed by mathematical induction.For the drive-response systems with disturbance,a time-varying impulsive control scheme is designed,and the drive-response systems is synchronized under the time-varying impulsive control.Then,the stability and synchronization of a class of new chaotic systems and hyperchaotic systems under time-varying impulsive control are considered,and the effectiveness of the results is proved by numerical analysis.