Continuous-Time Markov Networks: From Merging Rules to Synchronizing Control

• 成果类型: Article
• 署名作者: Li, Changxi; Lin, Lin; Xiong, Wenjun; Lam, James; Kwok, Ka-Wai
• 署名单位: Shandong University; East China University of Science and Technology; University of Hong Kong; University of Electronic Science & Technology of China; University of Hong Kong; Chinese University of Hong Kong
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2025.3580684
• 发表日期: 2025
• 关键词: Boolean control networks; stabilization; STABILITY

摘要

This article characterizes the state-space representation and control Lyapunov theory for continuous-time Markov networks (CT-MNs), which constitute a family of Markov chains endowed with network structures, serving as the theoretical basis for the investigations of several swarm behaviors. First, the notions of coupling Markov property and conditional independent property are introduced, enabling a CT-MN to be merged as a decentralized continuous-time Markov chain (CT-MC). Then, explicit formulas for the transition rate matrix of the augmented CT-MCs are derived. Consequently, key problems in CT-MNs can be reformulated as set-stability or set-stabilization problems for the augmented CT-MCs, with feedback controllers designed via linear programming subject to Lyapunov-based stability constraints. Furthermore, leader-follower synchronization and output regulation of CT-MNs are addressed. Finally, numerical examples validate the theoretical results and demonstrate their effectiveness in practical applications.