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

This paper 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...

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Bibliographic Details
Published inIEEE transactions on automatic control pp. 1 - 16
Main Authors Li, Changxi, Lin, Lin, Xiong, Wenjun, Lam, James, Kwok, Ka-Wai
Format Journal Article
LanguageEnglish
Published IEEE 2025
Subjects
Aerospace electronics
Continuous-time Markov networks
control Lyapunov functions
Convergence
Couplings
Main-secondary
Markov chains
Markov random fields
master-slave synchronization
Mathematical models
output regulation
Regulation
state space representation
Synchronization
Transmission line measurements
Vectors
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ISSN0018-9286
1558-2523
DOI10.1109/TAC.2025.3580684

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Summary:This paper 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, master slave synchronization and output regulation of CT-MNs are addressed. Finally, numerical examples validate the theoretical results and demonstrate their effectiveness in practical applications.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2025.3580684