Research On Containment Control Of Multiagent Systems Under Heterogeneous Networks And Signed Networks

With the development of science and technology,the problems that people facing are more and more complicated,which also promote the continuous cross-combination of various disciplines such as computer technology,communication technology,etc.Multi-agent systems have attracted widespread attention from scholars for their simple maneuverability and superior task completion capabilities in practical applications,and the cooperative control of multi-agent systems emerges as the times require.The containment control of multi-agent systems is a important branch of cooperative control of multi-agent systems.And it has a wide application prospects in ground exploration,logistics transportation,and military fields.Under this background,based on graph theory,matrix analysis theory,algebra knowledge,stability theory of linear system and corresponding agent control algorithm,this paper studies the containment control of multi-agent systems under different communication networks.In the process of realizing the containment control of multi-agent systems,the communication network of the systems may be disturbed by some factors and become unstable,and the stabilities of the systems will be affected accordingly.This paper investigates the containment control problems of second-order multi-agent systems under switching heterogeneous networks,where the follower position topologies are undirected,and the velocity topologies are directed.Two cases are considered: position topologies are jointly connected when velocity topology is fixed,and velocity topologies switch over time when position topology is fixed.The corresponding containment control protocols are designed for these two cases.By combining Lyapunov stability theory,La Salle's invariance principle and Cauchy's convergence criteria,the sufficient conditions for the multi-agent systems to realize containment control are given.Under the proposed control protocols,the velocities of the followers will be consistent with that of the leaders,and the followers will eventually converge into the convex hull spanned by the leaders.Furthermore,the simulation results verify the feasibility and effectiveness of the proposed algorithm.This paper further considers the situation that there are not only cooperation relationships but also antagonistic relationships between agents,and takes the general linear dynamic equation as the research object.The stabilizability and bipartite containment control problems of general linear multi-agent systems over signed directed graphs is further investigated,where the negative edges indicate the antagonistic interactions between agents.Employing the proposed bipartite containment control protocols over signed directed graphs,and combining the linear system stabilization theory and the signed Laplacian matrix,the necessary condition for the stabilization of multi-agent systems with multiple leaders is discussed.According to this condition,a leader-follower matching method is presented to establish leader-follower multiagent system networks.Based on the leader-follower topologies established above and the designed state feedback gain,the stability of multi-agent systems is proved by employing the system error and the algebraic Riccati equation.It is shown that the followers can gradually converge into the convex hull spanned by the states and the sign-inverted states of the leaders,and the whole systems can realize bipartite containment control.The simulation results verify the feasibility of the theoretical analysis.