Study On The Group Consensus Of Discrete-time Mixed-order Multi-agent Systems

With the development of information technology,many researchers have paid their attention to the consensus of multi-agent systems.Due to the differences of the environment where the agents are located and the goals that different agents expect to achieve,the consensus states of all agents in the same multi-agent system will be different.The group consensus of discrete-time mixed-order multiagent systems is studied in this paper.The contributions of the paper are summarized as follows:1.A special kind of group consensus is studied for mixed-order multi-agent systems composed of discrete-time first-and second-order agents under fixed and switching topologies,respectively;where the position states of first-order agents reach one consensus value while the position states of secondorder agents reach another consensus value.In the analysis,communication delays are considered.To solve the group consensus problem,group consensus protocols are firstly proposed.Then,by introducing model transformation,the group consensus of closed-loop system is transformed into the consensus of the equivalent system.Under certain assumptions,the conditions for asymptotic group consensus of mixed-order multi-agent systems are given by applying algebraic graph theory and matrix theory.Finally,the validity of the theoretical results is verified by numerical simulations.2.The s-group consensus of mixed-order multi-agent systems proposed in problem 1 is investigated under fixed topology.The group consensus protocols are also proposed.Under certain assumptions,graph theory and matrix theory are utilized to derive the conditions for guaranteeing the asymptotic s-group consensus of mixed-order multi-agent systems.In this kind of group consensus problems,agents with the same task belong to the same group,and agents with different tasks belong to different groups.Numerical examples verify the validity of the theoretical results.3.Following the work in problem 2,the s-group consensus problem is also addressed for discretetime mixed-order multi-agent systems with communication delays.Group consensus protocols are designed for first-order agents and second-order agents,respectively.Under certain assumptions,sufficient conditions are given for discrete-time mixed-order multi-agent systems with fixed topology to reach s-group consensus by using graph theory,matrix theory as well as Nyquist stability criterion.Finally,simulations are carried out to verify the validity of the theoretical results.