Sarymsakov Matrices and Asynchronous Implementation of Distributed Coordination Algorithms

We provide new insight into the somewhat obscure definition of the Sarymsakov class of stochastic matrices and use it to construct a new necessary and sufficient condition for the convergence of products of stochastic matrices. Such convergence result is critical in establishing the effectiveness of...

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Bibliographic Details
Published in:IEEE transactions on automatic control Vol. 59; no. 8; pp. 2228 - 2233
Main Authors: Xia, Weiguo, Cao, Ming
Format: Journal Article
Language:English
Published: New York IEEE 01.08.2014
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Agents (artificial intelligence)
Algorithm design and analysis
Algorithms
Asynchronous events
Automatic control
Clocks
Convergence
distributed coordination
Expert systems
Indexes
Multi-agent systems
Sarymsakov matrices
scrambling matrices
Stochastic processes
Stochasticity
Synchronization
Tasks
Vectors
ISSN:0018-9286, 1558-2523, 1558-2523
Online Access:Get full text
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Summary:We provide new insight into the somewhat obscure definition of the Sarymsakov class of stochastic matrices and use it to construct a new necessary and sufficient condition for the convergence of products of stochastic matrices. Such convergence result is critical in establishing the effectiveness of distributed coordination algorithms for multi-agent systems and enables us to investigate a specific coordination task with asynchronous update events. The set of scrambling stochastic matrices, a subclass of the Sarymsakov class, is utilized to establish the convergence of the agents' states even when there is no common clock for the agents to synchronize their update actions.
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ISSN:0018-9286
1558-2523
1558-2523
DOI:10.1109/TAC.2014.2301571