### Containment Control of Multi-Agent Systems with Stochastic Multiplicative Noises

REN Junhao1,2,3, ZONG Xiaofeng1,2,3

1. 1. School of Automation, China University of Geosciences, Wuhan 430074, China;2. Hubei Key Laboratory of Advanced Control and Intelligent Automation for Complex Systems, Wuhan 430074, China;3. Engineering Research Center of Intelligent Technology for Geo-Exploration, Ministry of Education, Wuhan 430074, China
• Received:2020-07-28 Revised:2020-12-07 Published:2022-06-20
• Supported by:
This paper was supported in part by the National Natural Science Foundation of China under Grant No. U1911401.

REN Junhao, ZONG Xiaofeng. Containment Control of Multi-Agent Systems with Stochastic Multiplicative Noises[J]. Journal of Systems Science and Complexity, 2022, 35(3): 909-930.

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.