Research On Bipartite Consensus Of Multi-agent Systems Based On Discontinuous Control Strategies

Multi-agent systems has been widely used in various fields because of its strong robustness,fault tolerance and scalability.Multi-agent systems can accomplish many complex tasks through cooperation.Therefore,the research on cooperative control of multiagent systems has become a current research hotspot.Based on the previous achievements,the cooperative control of multi-agent systems with various dynamic models are investigated in this paper,meanwhile,the problems of bipartite consensus and scaled bipartite consensus of multi-agent systems are discussed by various discontinuous control strategies.In addition,numerical simulations are used to illustrate the validity and correctness of the theories and methods discussed in this paper.The main works of this paper can be summarized as follows:1.The problems of scaled bipartite consensus of multi-agent systems with mixed time delays are researched deeply.Firstly,in light of the relevant knowledge of differential inequalities,a lemma about the convergence of differential equations with time delays is summarized and proved,which provides a better theoretical basis for the application of intermittent control strategies in control theory.Secondly,for the second-order multi-agent system with mixed time delay,a periodic intermittent control algorithm with sliding gain is proposed.With the help of Jensen's inequality,matrix theory and the relevant knowledge,the scaled bipartite consensus criteria of the second-order multi-agent systems with mixed time delay are obtained.2.The state compensation and bipartite consensus problems of nonlinear second-order multi-agent systems are considered.For a second-order multi-agent systems with nonlinear characteristics,a periodic intermittent control algorithm is proposed based on state compensation.When the measurement velocity states of the second-order systems cannot be obtained directly,a fully distributed state compensator is designed based on the measurement output of the system,and the relative measurement error of the system is estimated through the compensation,meanwhile,the specific selection method of the controlled agents is provided.Finally,the bipartite consensus criteria of the nonlinear second-order multi-agent systems are obtained.3.For the first-order linear multi-agent systems,the problems of bipartite consensus by two types of event-triggered control are analyzed and studied.Firstly,considering the linear multi-agent systems without a leader,the triggering condition based on combined measurement error and the event-triggered control protocol based on relative information perception are constructed.According to the relevant properties of the Riccati equation solution,the bipartite consensus criteria are obtained,meanwhile Zeno phenomenon will not occur.In addition,for the leader-follow multi-agent systems,corresponding triggering condition and event-triggered control protocol are proposed.4.For general nonlinear second-order multi-agent systems,the event-triggered bipartite consensus strategies are deeply studied for second-order systems.Firstly,a completely distributed fixed control gain event-triggered control protocol and triggering condition are analyzed and proposed.With the help of matrix inequality and control theory,the bipartite consensus criteria are obtained and the Zeno phenomenon can be avoided.Secondly,a fully distributed sliding gain event-triggered control protocol is considered,and the corresponding bipartite consensus criteria are obtained.To sum up,the application of various discontinuity control strategies under different dynamic models are studied,the state evolution characteristics of multi-agent systems under the influence of nonlinear functions,time delay and other factors are discussed deeply.In addition,the proposed research results are verified by numerical simulations.At the end of this paper,the main works of this paper are summarized,and the future research direction is prospected.