Consensus For Heterogeneous Multi-agent Systems

Currently,distributed coordination control problems for multi-agent systems have attracted much attention,due to its broad applications,such as sensor configuration,congestion control,formation,aerospace,etc.One of the fundamental problems is consensus.The consensus for multi-agent systems means that the states of all the agents converge to a common value by negotiating with their neighbors asymptotically or in a finite time without centralized control.A central idea to realize the consensus for multi-agent systems is to design proper control law for each agent by using local information from its neighbors.According to the existing conclusion,the dynamics of agents considered are mostly in the same order.Actually,the dynamics of agents coupled with each other could be different because of various restraints or the common goals with mixed agents.In this paper,we have studied the consensus problem of heterogeneous multi-agent systems composed of first-order and second-order agents.In this paper,based on the research of related scholars,we have discussed the issues of consensus for heterogeneous multi-agent systems by using the algebra theory,stability theory,control theory,matrix theory and other related knowledge.Firstly,for the cases that the heterogeneous multi-agent system with and without time-delay,we have studied the consensus problem under fixed and switching topologies.Many experts focus on the conditions of consensus,instead seeking the equilibrium point.In some cases,the equilibrium state of the systems is uncertain.In this thesis,by a system transformation method,the system is described by an uniform matrix.By analyzing the matrix,the final equilibrium state can be expressed with the characteristic vector of Laplacian matrix and the initial state representation.Similar conclusion can be applied to the system with bounded communication delay.Secondly,the frequency domain analysis of the consensus for the discrete-time heterogeneous multi-agent systems with time delay has been carried out.For the cases that systems without delay,having the input delay and having both communication delays and input delays at the same time have been investigated.During the process,the relative analysis of time-domain is converted into the frequent-domain.Graph theory,stable theory and frequent domain analysis methods have been used for the cases that the consensus problem with diverse delays and different topologies.Finally,group consensus for heterogeneous multi-agent systems has been studied.Different protocols are designed for different dynamic agents.The problem of the consistency for the complex heterogeneous multi-agent system is transformed into the stability problem of the homogeneous system.The parameters of the system under fixed topology are obtained by using algebraic graph theory and stability theory.When the system contained uniformly bounded input delays,the Lyapunov functions are constructed properly.The sufficient conditions for the consistency of the systemare given by using the linear matrix inequality approach.