Research And Application Of Robust Consensus Algorithm For Multi-agent Systems

Because of good redundancy, robustness and autonomy in multi-agent systems, multi-agent systems which complete complex tasks through coordination between individuals become a hot issue in recent years. As a fundamental problem in multi-agent systems, consensus means that all the agents in systems eventually converge to a common state through interactions of all individuals.In this paper, consensus problems for multi-agent systems with time-delay are considered. By using algebraic graph theory and Lyapunov stability theory, consensus problems for first-order multi-agent systems and second-order multi-agent systems has been considered in this thesis. Main research contents are listed as following:1) Consensus problem of first-order multi-agent systems with time varying delays. Under the assumption that the undirected communication topology is fixed and connected, firstly, the original system with n dimensions can be divided into two subsystems through orthogonal transformation:a one-dimensional system and a n-1dimensional system; secondly, Lyapunov function and Lyapunov stability theory are employed to derive the sufficient condition for consensus of multi-agent systems.2) Based on above model, robust H∞consensus for multi-agent systems with disturbances and uncertain parameters has been considered.Based on the characteristic of Laplacian matrix in undirected and connected graph, system model has been transformed into two low dimensional subsystems. Suitable Lyapunov function for low-dimensional system has been constructed to solve time-delays. Consensus problem with disturbances and uncertain parameters has been solved by designing control law. Finally, sufficient condition for robust H∞consensus of multi-agent systems has been obtained with LMI tool.3) Consensus problem of second-order multi-agent systems with time delay and nonlinear dynamics.Algorithm for solving consensus of second-order multi-agent systems with time delay and nonlinear dynamics is proposed. Based on the feature of nonlinear dynamics, nonlinear system is transformed into a linear system. By constructing Lyapunov function and using Lyapunov stability theory, a sufficient condition for consensus of second order multi-agent systems with nonlinear dynamics has been obtained.4) Consensus on reference model of second-order multi-agent systems with time delay and nonlinear dynamics.The steady values of all agents are not limited to a constant but reaching consensus on some desired reference model in consensus problem of this section. Algorithm for solving model reference consensus of second-order multi-agent systems with time delay and nonlinear dynamics is proposed. Based on previous results of linear systems and Lyapunov stability theory, sufficient condition has been obtained in consensus on reference model for multi-agent systems with time delay and nonlinear dynamics.