Containment control for distributed networks subject to multiplicative and additive noises with stochastic approximation–type protocols

• Published in: International journal of robust and nonlinear control Vol. 30; no. 2; pp. 665 - 684
• Main Authors: Du, Yingxue, Wang, Yijing, Zuo, Zhiqiang, Zhang, Wentao
• Format: Journal Article
• Language: English
• Published: Bognor Regis Wiley Subscription Services, Inc 25.01.2020
• Subjects: Approximation; Computer networks; Containment; containment control; Convergence; dynamical leaders; Economic models; Mathematical analysis; multiplicative and additive noises; Protocol (computers); stochastic approximation
• ISSN: 1049-8923; 1099-1239
• DOI: 10.1002/rnc.4791

Summary This paper is concerned with the stochastic containment control problem for distributed network with multiplicative and additive noises, in which the stochastic approximation technique is utilized. A major challenge, compared with the existing results with multiplicative and additive noises, is that the involving leaders are dynamically changing. It is shown that finite boundedness for dynamical leaders is of great importance for addressing the stochastic containment control issue. A suitable approach is proposed to handle multiplicative and additive noises based on the stochastic approximation, and some necessary/sufficient conditions are derived for mean square convergence with mild requirements. Furthermore, the convergence rates are studied for both dynamical leaders and static leaders scenarios. We conclude this paper by using two illustrative examples to verify the effectiveness of the theoretical results.