Impulsive consensus of one-sided Lipschitz nonlinear multi-agent systems with Semi-Markov switching topologies |
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Institution: | 1. School of Science, Beijing Technology and Business University, Beijing 100048, PR China;2. Department of Mathematics, Beijing Jiaotong University, Beijing 10044, PR China;1. Faculty of Science, Yibin University, Yibin, Sichuan 644000, China;2. College of Electronic and Information Engineering, Southwest University, Chongqing 400715, China;3. School of Mathematical and Statistics, Southwest University, Chongqing 400715, China;4. School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China |
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Abstract: | Many real systems involve not only parameter changes but also sudden variations in environmental conditions, which often causes unpredictable topologies switching. This paper investigates the impulsive consensus problem of the one-sided Lipschitz nonlinear multi-agent systems (MASs) with Semi-Markov switching topologies. Different from the existing modeling methods of the Markov chain, the Semi-Markov chain is adopted to describe this kind of randomly occurring changes reasonably. To cope with the communication and control cost constraints in the multi-agent systems, the distributed impulsive control method is applied to address the leader–follower consensus problem. Beyond that, to obtain a wider nonlinear application range, the one-sided condition is delicately developed to the controller design, and the results are different from the ones obtained in the traditional method with the Lipschitz condition (note that the existing results are usually only applicable to the case with small Lipschitz constant). Based on the characteristics of cumulative distribution functions, the theory of Lyapunov-like function and impulsive differential equation, the asymptotically mean square consensus of multi-agent systems is maintained with the proposed impulsive control protocol. Finally, an explanatory simulation is presented to validate the correctness of the proposed approach conclusively. |
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Keywords: | Multi-agent systems Impulsive consensus Semi-Markov switching topologies One-sided Lipschitz conditions |
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