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Asymptotic properties of consensus-type algorithms for networked systems with regime-switching topologies
- Source :
-
Automatica . Jul2011, Vol. 47 Issue 7, p1366-1378. 13p. - Publication Year :
- 2011
-
Abstract
- Abstract: This paper is concerned with asymptotic properties of consensus-type algorithms for networked systems whose topologies switch randomly. The regime-switching process is modeled as a discrete-time Markov chain with a finite state space. The consensus control is achieved by using stochastic approximation methods. In the setup, the regime-switching process (the Markov chain) contains a rate parameter in the transition probability matrix that characterizes how frequently the topology switches. On the other hand, the consensus control algorithm uses a stepsize that defines how fast the network states are updated. Depending on their relative values, three distinct scenarios emerge. Under suitable conditions, we show that when , a continuous-time interpolation of the iterates converges weakly to a system of randomly switching ordinary differential equations modulated by a continuous-time Markov chain. In this case a scaled sequence of tracking errors converges to a system of switching diffusion. When , the network topology is almost non-switching during consensus control transient intervals, and hence the limit dynamic system is simply an autonomous differential equation. When , the Markov chain acts as a fast varying noise, and only its averaged network matrices are relevant, resulting in a limit differential equation that is an average with respect to the stationary measure of the Markov chain. Simulation results are presented to demonstrate these findings. [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 00051098
- Volume :
- 47
- Issue :
- 7
- Database :
- Academic Search Index
- Journal :
- Automatica
- Publication Type :
- Academic Journal
- Accession number :
- 60789198
- Full Text :
- https://doi.org/10.1016/j.automatica.2011.02.028