Research On Group Consensus Of Second-order Multi-agent Systems And Consensus Of Mixed-order Multi-agent Systems

This dissertation investigates the group consensus problem for second-order multi-agent systems as well as the consensus problem for a class of mixed-order multi-agent systems. As to the group consensus of continuous-time and discrete-time multi-agent systems, group consensus protocols are proposed, and algebraic conditions and parameter conditions for guaranteeing group consensus are presented. The expressions of group consensus states are specified. As to the consensus of mixed-order multi-agent systems, we focus on the design of linear and nonlinear consensus protocols, analysis of the consensus criteria and solution to the expressions of the consensus states. Tools like matrix theory, graph theory, linear system theory, finite-time Lyapunov theory are applied in our research. The contributions of this dissertation are summarized as follows:1. The group consensus problem for continuous-time second-order multi-agent systems with fixed and directed communication topology is studied. Three different kinds of group consensus protocols are proposed to solve the dynamic and static group consen-sus problems, respectively. Under mild assumptions, matrix theory is used to analyze the eigenvalues of the system matrix of the closed-loop system. Some necessary and sufficient conditions are given to make the multi-agent systems reach couple-group con-sensus. The specific expressions of the final states are also given. Furthermore, we consider the effects of control parameters and communication topology on group con-sensus. Relevant results are extended to solve the muti-group consensus problem for second-order multi-agent systems. Numerical examples are given to validate the effec-tiveness of proposed protocols and theoretical results.2. The group consensus problem for discrete-time second-order multi-agent systems with fixed and directed communication topology is addressed. Sampling period is consid-ered in analyzing the group consensus problem for discrete-time multi-agent systems. Couple-group consensus problem for discrete-time second-order multi-agent systems is firstly studied. The main research includes proposing the consensus protocols, analyz-ing the properties of the system matrix of the closed-loop system by using matrix theory and linear system theory, deriving conditions for ensuring couple-group consensus and presenting the expressions of group consensus states. For a given communication topol-ogy, we provide an efficient way on how to find proper control parameters and sampling period to guarantee couple-group consensus by using matrix theory and the stability the-ory of polynomial with complex coefficients. Then, consensus protocols are revised to solve the multi-group consensus problems. Algebraic conditions as well as parameter- dependent conditions are given for solving the multi-group consensus problem. Numer-ical examples indicate the effectiveness of the theoretical results.3. The asymptotic consensus problem for a class of mixed-order multi-agent systems with directed communication topology is considered, where the multi-agent system is com-posed of second-order agents and first-order agents. A general linear consensus protocol is studied and a necessary and sufficient condition on communication topology is given based on matrix theory and well-known results on first-order multi-agent systems. The consensus states are also specified. For the case of switching communication topologies, a sufficient condition is presented for information consensus by using the properties of the products of the row-stochastic matrices. Numerical examples are provided to demon-strate the effectiveness of the theoretical results.4. The consensus problem for a class of mixed-order multi-agent systems is considered under two kinds of communication topologies:undirected, connected topology and strongly connected topology satisfying the detailed balance condition, where nonlin-ear consensus protocols are proposed for the second-order agents and first-order agents, respectively. By utilizing the Lyapunov theory, LaSalle’s invariance principle and homo-geneous system theory, it is proved that mixed-order multi-agent systems can reach con-sensus in a finite time by applying proposed consensus protocols. Then, the finite-time consensus protocols are revised, with which multi-agent systems will reach consensus asymptotically. And some invariant quantities are introduced to derive the expressions of the consensus states. Numerical examples are presented to illustrate the effectiveness of the theoretical results.