Containment Control of Multi-Agent Systems with Stochastic Multiplicative Noises

• Published in: Journal of systems science and complexity Vol. 35; no. 3; pp. 909 - 930
• Main Authors: Ren, Junhao, Zong, Xiaofeng
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2022; Springer Nature B.V
• Subjects: Complex Systems; Containment; Control; Graph theory; Liapunov functions; Mathematics; Mathematics and Statistics; Mathematics of Computing; Multiagent systems; Operations Research/Decision Theory; Statistics; System effectiveness; Systems Theory; stochastic system; multi-agent system; multiplicative noises; Containment control
• ISSN: 1009-6124; 1559-7067
• DOI: 10.1007/s11424-021-0167-4

This paper investigates the containment problem of continuous-time multi-agent systems with multiplicative noises, where the first-order and second-order multi-agent systems are studied respectively. Based on stochastic analysis tools, algebraic graph theory, and Lyapunov function method, the containment protocols based the relative states measurement with multiplicative noises are developed to guarantee the mean square and almost sure containment. Moreover, the sufficient conditions and necessary conditions related to the control gains are derived for achieving mean square and almost sure containment. It is also shown that multiplicative noises may works positively for the almost sure containment of the first-order multi-agent systems. Simulation examples are also introduced to illustrate the effectiveness of the theoretical results.