Projective Group Consensus of Multi-Agent Systems with Arbitrary Parameter
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Projective Group Consensus of Multi-Agent Systems with Arbitrary Parameter∗ CHEN Liangkang · GUO Liuxiao · YANG Yongqing
DOI: 10.1007/s11424-020-9137-5 Received: 25 April 2019 / Revised: 4 September 2019 c The Editorial Office of JSSC & Springer-Verlag GmbH Germany 2020 Abstract In this paper, the projective group consensus issue for second order multi-agent systems (MASs) in directed graphs with a dynamic leader is investigated. The proposed projective group consensus with arbitrary parameter includes traditional consensus, reverse group consensus and cluster consensus as its special cases. Novel distributed control protocols are designed to obtain projective group consensus without analyzing signed directed graph as in most current literatures on bipartite consensus problem. On the basis of Lyapunov stability property, algebraic graph and some necessary matrix theory, sufficient conditions for delay and delay-free cases are derived. Finally, simulations of nonlinear chaotic MASs are adopted to testify the theoretical results. Keywords
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Group consensus, multi-agent systems, subgroups, time delay.
Introduction
Nowadays, with the rapid development of artificial intelligence technology and its wide application in real life, scholars pay more and more attention to multi-agent systems (MASs). Of particular interest to scholars is how coordinated group behavior emerges in such network systems. Momentous effort has been made to investigate the mechanisms of consensus, synchronization, swarming and flocking. As is well known, there are a great deal of reports on the consensus of first-order MAS[1–4] . Furthermore, deep understanding of the second-order[5–7] consensus may result in drawing more realistic dynamics into the model of each individual agent on the foundation of the common framework for MASs, which is especially significant for the implementation of cooperative control strategies in biological and information engineering network systems. Different from the CHEN Liangkang · GUO Liuxiao (Corresponding author) · YANG Yongqing School of Science, Jiangnan University, Wuxi 214122, China. Email: [email protected]. ∗ This research was supported by the National Natural Science Foundation of China under Grant Nos. 61807016 and 61772013, the Natural Science Foundation of Jiangsu Province under Grant Nos. BK20181342 and BK20171142. This paper was recommended for publication by Editor LIU Guoping.
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CHEN LIANGKANG · GUO LIUXIAO · YANG YONGQING
first-order dynamics, which always converge to the unique limit, the second-order consensus protocols converge the information states to two distinct consistent values that one corresponding to the location and the other corresponding to the speed. In the discussion of problem for group consensus[8–10] , all the agents given are divided into two or more subgroups, and different subgroups reach different common state asymptotically. In complex practical applications of network control systems, due to cooperative task allocation and some changes in external environment, the agen
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