Stochastic approximation for consensus over general digraphs with Markovian switches

This paper considers consensus problems with Markovian switching networks and noisy measurements, and stochastic approximation is used to achieve mean square consensus. The main contribution of this paper is to obtain ergodicity results for backward products of degenerating stochastic matrices with Markovian switches, and subsequently prove mean square consensus for the stochastic approximation algorithm. Our ergodicity proof is to build a higher dimensional dynamical system and exploit its two-scale feature.

[1]  Tao Li,et al.  Mean square average-consensus under measurement noises and fixed topologies: Necessary and sufficient conditions , 2009, Autom..

[2]  John S. Baras,et al.  Almost sure convergence to consensus in Markovian random graphs , 2008, 2008 47th IEEE Conference on Decision and Control.

[3]  L. Elsner,et al.  On the convergence of asynchronous paracontractions with application to tomographic reconstruction from incomplete data , 1990 .

[4]  Ji-Feng Zhang,et al.  Stochastic Approximation Based Consensus Dynamics over Markovian Networks , 2015, SIAM J. Control. Optim..

[5]  Li Tao,et al.  Mean square average consensus of multi-agent systems with time-varying topologies and stochastic communication noises , 2008, 2008 27th Chinese Control Conference.

[6]  Soummya Kar,et al.  Distributed Consensus Algorithms in Sensor Networks With Imperfect Communication: Link Failures and Channel Noise , 2007, IEEE Transactions on Signal Processing.

[7]  Kenneth E. Barner,et al.  Convergence of Consensus Models With Stochastic Disturbances , 2010, IEEE Transactions on Information Theory.

[8]  John N. Tsitsiklis,et al.  Distributed Asynchronous Deterministic and Stochastic Gradient Optimization Algorithms , 1984, 1984 American Control Conference.

[9]  F. Cucker,et al.  Flocking in noisy environments , 2007, 0706.3343.

[10]  Subhrakanti Dey,et al.  Stochastic consensus over noisy networks with Markovian and arbitrary switches , 2010, Autom..

[11]  R.W. Beard,et al.  Multi-agent Kalman consensus with relative uncertainty , 2005, Proceedings of the 2005, American Control Conference, 2005..

[12]  Minyi Huang,et al.  Stochastic Approximation for Consensus: A New Approach via Ergodic Backward Products , 2012, IEEE Transactions on Automatic Control.

[13]  Martin J. Wainwright,et al.  Network-Based Consensus Averaging With General Noisy Channels , 2008, IEEE Transactions on Signal Processing.

[14]  R. P. Marques,et al.  Discrete-Time Markov Jump Linear Systems , 2004, IEEE Transactions on Automatic Control.

[15]  Gang George Yin,et al.  Consensus Formation in a Two-Time-Scale Markovian System , 2009, Multiscale Model. Simul..

[16]  R. Srikant,et al.  Quantized Consensus , 2006, 2006 IEEE International Symposium on Information Theory.

[17]  E. Seneta Non-negative Matrices and Markov Chains , 2008 .

[18]  Jonathan H. Manton,et al.  Stochastic Consensus Seeking With Noisy and Directed Inter-Agent Communication: Fixed and Randomly Varying Topologies , 2010, IEEE Transactions on Automatic Control.

[19]  J. Wolfowitz Products of indecomposable, aperiodic, stochastic matrices , 1963 .

[20]  Milos S. Stankovic,et al.  Decentralized Parameter Estimation by Consensus Based Stochastic Approximation , 2011, IEEE Trans. Autom. Control..