Bipartite Consensus Of Linear Multi-agent Systems

Multi-agent systems are important research objects in the field of artificial intelligence,which are composed of multiple agents that can perceive each other and have the ability to process information independently.As the most representative group behavior in multi-agent systems,consensus means that all agents tend to be in the same state after a period of time through the interaction of individuals.In multi-agent systems,there may be both cooperation and competition.In view of this,based on event-triggered control,constant coefficient feedback control and finite-time observation control,the bipartite consensus problem of multi-agent systems with cooperative and competitive interactions is studied in this thesis.The primary contents are as follows:In the first part,the fixed-time bipartite consensus of first-order multi-agent systems is studied with time delay and interference.Firstly,a kind of fixed-time eventtriggered controller is designed over the undirected signed graph.Particularly,the oscillation caused by the sign function is avoided by adding a saturation function to the controller.Then,using algebraic graph theory,fixed-time stability theory and set-value Lie derivative,it is proved that the system can achieve fixed-time bipartite consensus.In addition,the system does not produce Zeno behavior under the proposed event-triggered algorithm.Finally,two numerical examples are given to verify the correctness of theoretical analysis.In the second part,the leader-following bipartite consensus of second-order multiagent systems is studied with a leader.Firstly,two bipartite controllers containing a sign function and a saturation function are designed respectively over the undirected signed graph.Then,using the Lyapunov stability theory and La Salle's invariance principle,it is proved that the system can reach the bipartite consensus.Finally,numerical simulation is performed to verify the effectiveness of the control protocol under three different topology structures.In the third part,the finite-time bipartite output consensus of leader-following heterogeneous linear multi-agent systems is studied with and without interference.Firstly,based on the information exchange between agents,the finite-time stability theory and Riccati equation,the compensator is constructed to estimate the state information of leader over the directed signed graph.Secondly,a finite-time bipartite controller is designed based on the output feedback control and the finite-time control so that the system can achieve finite-time bipartite consensus.Moreover,a novel finite-time bipartite control protocol is proposed for the multi-agent systems with measurable interference by using observation-based feedback control.Finally,the validity of the two protocols is verified in numerical simulation.