Abstract
This paper investigates the mean square consensus problem of multi-agent systems impacted by the combined uncertainty of multiplicative noises and time delays. Considering general network under directed fixed topologies, we propose consensus protocol that take into account both the multiplicative noises and time delays. Using tools from stochastic differential delay equation (SDDE), martingale theory and stochastic inequality, we establish sufficient conditions and obtain the explicit consensus gain and delay upper bounds under which the proposed protocol leads to mean square consensus. In addition, we compare the impact of multiplicative and additive noise and reach the conclusion that multiplicative noises have the property of stabilizing effect. Simulations demonstrate the theoretical results.
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Recommended by Guest Editors PooGyeon Park and Ju H. Park. This work was supported by the Shanghai Pujiang Program under grant 15PJ1404300.
Lei Song is a Ph.D. student with the School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai, China. His research interests include distributed control theory and multi-agent systems.
Dan Huang received his Ph.D. degree from The University of Auckland, New Zealand, in 2008. Now he is an Associate Professor at Shanghai Jiao Tong University, Shanghai, China. His research interests include distributed control theory and networked control systems.
Sing Kiong Nguang received his Ph.D. degree from The University of Newcastle, Australia in 1995. Now he is a Professor at The University of Auckland, Auckland, New Zealand. His research interests include polynomial control systems and networked control systems.
Shan Fu received his Ph.D. degree from Heriot-Watt University, U.K., in 1995. Now he is a Professor at Shanghai Jiao Tong University, Shanghai, China. His research interests include complex systems and human factors.
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Song, L., Huang, D., Nguang, S.K. et al. Mean square consensus of multi-agent systems with multiplicative noises and time delays under directed fixed topologies. Int. J. Control Autom. Syst. 14, 69–77 (2016). https://doi.org/10.1007/s12555-015-2010-y
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DOI: https://doi.org/10.1007/s12555-015-2010-y