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Stochastic consensus of discrete-time second-order multi-agent systems with measurement noises and time delays. (English) Zbl 1393.93014
Summary: We study the consensus control of discrete-time second-order multi-agents systems with time delays and multiplicative noises, where the consensus protocol is designed by both the local relative position measurements and each agent’s absolute velocity. Due to the existence of time delays and multiplicative noises, the classical methods for deterministic models with time delays cannot work. In this paper, we apply stochastic stability theorem of discrete-time stochastic delay equations to find some explicit sufficient conditions for both mean square and almost sure consensus. It is proven that for any given noise intensities and time delays, the second-order multi-agent consensus can be achieved by choosing appropriate control gains in the relative position measurement and absolute velocity, respectively. Numerical simulation is given to demonstrate the effectiveness of the proposed protocols as well as the theoretical results.
##### MSC:
 93A14 Decentralized systems 93C55 Discrete-time control/observation systems 68T42 Agent technology and artificial intelligence 93E15 Stochastic stability in control theory
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