Research On Multi-agent Pinning Consistency Considering Control Energy Optimization

With the rapid development of multi-agent systems,the problems involved are becoming more and more complicated,which also promotes the continuous cross-integration between various disciplines.In practical applications,multi-agent consensus,as an important branch of system control,has been widely used in satellite,smart grid,ground survey and other related fields.However,the control energy problem in the process of system consensus has not been studied in depth.In this context,based on graph theory,matrix analysis,network science theory and algebraic knowledge,this paper designs agent control algorithms with different pinning effects,and studies the optimal control energy problem of multi-agent consensus under pinning control.Considering the influence of the cooperation-competition relationship between followers and leaders on the final convergence state of symbolic network agents when multi-agent systems achieve fixed-time and preset-time bipartite consensus,this paper studies the bipartite consensus pinning problem of multi-agents under fixed-time and preset-time.In addition,the control energy problem of multi-agent bipartite consensus is explored for different output configurations.Firstly,the control energy is combined with the fixed time and preset time bipartite consensus pinning control of multi-agent,and the energy difference under different output configurations is considered.Secondly,based on the signed network multi-agent system with structural balance,the strategy of reducing control energy by optimizing output configuration under target controllability is given.Then,according to the Lyapunov stability theory,the fixed-time and preset-time bipartite consensus control protocols of multi-agent under pinning control are designed respectively,so that the agent can achieve the bipartite consensus of the same or opposite state as the leader under the proposed control protocol.Subsequently,the feasibility of the proposed algorithm is verified by numerical simulation.In this paper,the control energy problem of multi-agent systems with cooperative-competitive relationship in the realization of bipartite inclusion is further considered.The general linear dynamic equation is taken as the research object,and the methods of optimizing control energy under different pinning strategies are studied.Firstly,considering the control energy problem under different pinning effects in multi-agent containment control,the leader-following pinning strategy for control energy optimization and the control energy optimization strategy for eliminating the longest control chain in the network by adding key edges are given respectively.Then,according to the algebraic Riccati equation and Lyapunov stability theory,a bipartite containment control protocol for multi-agents in signed networks is designed,which can make the follower agent converge to the convex hull surrounded by the leader state and its anti-state under the control protocol.Finally,the correctness of the algorithm is verified by numerical simulation.