Sarymsakov matrices and their application in coordinating multi-agent systems
The convergence of products of stochastic matrices has proven to be critical in establishing the effectiveness of distributed coordination algorithms for multi-agent systems. After reviewing some classic and recent results on infinite backward products of stochastic matrices, we provide a new necessary and sufficient condition for the convergence in terms of matrices from the Sarymsakov class of stochastic matrices, which complements the known other necessary and sufficient conditions. To gain insight into the somewhat obscure definition of the Sarymsakov class, we generalize some conditions in the definition and prove that the resulted set of matrices is exactly the set of indecomposable, aperiodic, stochastic matrices that has been extensively studied in the past. To apply the gained knowledge about the Sarymsakov class to the coordination of multi-agent systems, we investigate a specific coordination task with asynchronous update events. Then the set of scrambling stochastic matrices, a subclass of the Sarymsakov class, is utilized to establish the convergence of the system’s state even when there is no common clock for the agents to synchronize their update actions.
Weiguo Xia Ming Cao
Faculty of Mathematics and Natural Sciences, ITM, University of Groningen, The Netherlands
国际会议
The 31st Chinese Control Conference(第三十一届中国控制会议)
合肥
英文
6321-6326
2012-07-01（万方平台首次上网日期，不代表论文的发表时间）