Consensus Analysis and Synthesis of Networked Multi-Agent Systems
As one of the major ﬁelds, Networked Multi-Agent Systems (NMAS), which deals with the study of how network architecture and interactions among network components inﬂuence global control goals, has received widely attention across science and engineering. A usual problem that appears in the coordination of NMAS is the consensus problem, i.e., given initial values (scalar or vector) of agents, establish conditions under which through local interactions and computations, the agents asymptotically achieve some kind of agreement, such as control of mobile vehicles, information processing in sensor networks and design of distributed algorithms. Researches mainly focused on the analysis of NMAS consensus in the past, the interconnection topology and some consensus algorithms were given in advance and the relevant research objective was to verify whether the states of all agents converge to some common value. Agents with single integrator dynamics, double integrator dynamics or more complicated dynamics are the present research emphasis. In addition, most of present research activities focus on theoretical study of consensus problems based on relatively simple simulation experiments, but it will still be a key element of research in the future. Although it is more complicated to consider consensus problems for a team of agents with more complex nonlinear dynamics and even heterogenous dynamics, such kind of problems are very important. To the best of our knowledge,there are few eﬀective results on this topic. Usually, no common equilibrium for all agents exists even if each isolated agent has an equilibrium, but an NMAS with non-identical agents may still exhibit some consensus behaviors which are from being fully understood. Certain reasonable and satisfactory boundedness of state motion errors between diﬀerent agents can be taken as useful consensus properties. This thesis focuses on the global consensus problems of NMAS consisting of identical or non-identical agent dynamics, and the proposed consensus property is formulated in terms of certain boundedness of state errors. Moreover, on specialoccasions, we still investigate their exact consensus conditions. Compared with many existing results, the thesis makes several signiﬁcant contributions. Firstly, we generalize the related results for the case of identical agent dynamics to the case of non-identical agent dynamics and the proposed results cover the existing criteria of networks with identical agent dynamics as special cases. Secondly, we consider the communication delay among the agents, global consensus criteria are given based on solving a number of lower dimensional matrix inequalities and scalar inequalities, which generalize the criteria using the method of the mas ter stability function for NMAS with identical agents. Finally, globally bounded consensus conditions for both delay-independent and delay-dependent conditions based on the Lyapunov-Krasovskii functional method are derived.
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