Multi-consistency And Convergence Performance Optimization Of Multi-agent Systems

With the development of computer technology,network communication,distributed control,3D printing and other technologies,multi-agent systems will have a broad application prospect.As a frontier problem in the research of multi-agent systems,its coordination control has been paid more and more attention by researchers in related fields.Multi-consensus of multi-agent systems provides a theoretical framework for coordination control of multi-task,multi-objective and multi-tracking complex multi-agent systems.In this dissertation,the rectangular wave control protocol is designed for both stationary multi-consensus and dynamic multi-consensus of multi-agent systems,and the convergence performance optimization of the multi-agent systems is considered.In addition,the multi-consensus problem of heterogeneous multi-agent systems is studied for communication topology with time-varying weights.The main research contents are summarized as follows:(1)The stationary multi-consensus of multi-agent systems and its convergence performance optimization are studied.A rectangular wave control protocol is designed with adjustable action time,a necessary and sufficient condition of multi-consensus problem is given based on Hurwitz stability criterion.Then,a parameter optimization algorithm is designed for the faster multi-consensus convergence rate via the dichotomy,and the minimum spectral radius of the multi-agent system is as the optimal index in the algorithm.Finally,based on the fixed communication topology,a numerical simulation is given to show the effectiveness of the rectangular wave control protocol proposed.These results show that if the suitable parameters of the rectangular wave control protocol are given,the multi-agent systems not only can achieve stationary multi-consensus,but also can improve the convergence rate greatly.(2)The dynamic multi-consensus problem of second order discrete multi-agent systems is studied based on rectangular wave control under convex topological sets.The positive and negative values of the adjacency matrix elements are used to represent the cooperative-competition between agents.Based on the algebraic graph theory,matrix theory and stability theory,the dynamic multi-consensus problem of multi-agent systems is transformed into the stability problem of linear discrete system.The convex combination of two topologies is used to show the various topologies after the network topology changes,and a set of topologies is obtained,the necessary and sufficient conditions for the system to achieve dynamic multi-consensus are also derived under the condition of the convex topology set.Finally,a numerical simulation example is provided to verify the effectiveness of the theoretical results.(3)The stationary multi-consensus of heterogeneous multi-agent systems with timevarying topological weights is considered.Based on the first and second order continuous time heterogeneous multi-agent systems,the control protocol related to agent position and speed is proposed,and the dynamic change of topology weight is described by the expression related to the distance between agents.The stability of heterogeneous multiagent error system is proved by using Lyapunov's second method,and then a sufficient condition is obtained for the realization of stationary multi-consensus in a heterogeneous multi-agent systems with time-varying topological weights,and the conditions that its control parameters need to meet.