Stochastic Consensus Seeking With Noisy and Directed Inter-Agent Communication: Fixed and Randomly Varying Topologies

We consider consensus seeking of networked agents on directed graphs where each agent has only noisy measurements of its neighbors' states. Stochastic approximation type algorithms are employed so that the individual states converge both in mean square and almost surely to the same limit. We further generalize the algorithm to networks with random link failures and prove convergence results.

[1]  J.H. Manton,et al.  Stochastic Lyapunov Analysis for Consensus Algorithms with Noisy Measurements , 2007, 2007 American Control Conference.

[2]  Maurizio Porfiri,et al.  Consensus Seeking Over Random Weighted Directed Graphs , 2007, IEEE Transactions on Automatic Control.

[3]  Reza Olfati-Saber,et al.  Consensus and Cooperation in Networked Multi-Agent Systems , 2007, Proceedings of the IEEE.

[4]  Alireza Tahbaz-Salehi,et al.  A Necessary and Sufficient Condition for Consensus Over Random Networks , 2008, IEEE Transactions on Automatic Control.

[5]  H. Teicher,et al.  Probability theory: Independence, interchangeability, martingales , 1978 .

[6]  Pierre Priouret,et al.  Adaptive Algorithms and Stochastic Approximations , 1990, Applications of Mathematics.

[7]  Harold J. Kushner,et al.  wchastic. approximation methods for constrained and unconstrained systems , 1978 .

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

[9]  E.M. Atkins,et al.  A survey of consensus problems in multi-agent coordination , 2005, Proceedings of the 2005, American Control Conference, 2005..

[10]  Jonathan H. Manton,et al.  Stochastic approximation for consensus seeking: Mean square and almost sure convergence , 2007, 2007 46th IEEE Conference on Decision and Control.

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

[12]  Panganamala Ramana Kumar,et al.  Toward a theory of in-network computation in wireless sensor networks , 2006, IEEE Communications Magazine.

[13]  J.H. Manton,et al.  Stochastic Double Array Analysis and Convergence of Consensus Algorithms with Noisy Measurements , 2007, 2007 American Control Conference.

[14]  Sanjeev R. Kulkarni,et al.  Weighted averaging and stochastic approximation , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

[15]  M. Loève On Almost Sure Convergence , 1951 .

[16]  Michel Loève,et al.  Probability Theory I , 1977 .

[17]  M. C. D. Oliveiraa,et al.  A new discrete-time robust stability condition ( , 1999 .

[18]  Randal W. Beard,et al.  Consensus seeking in multiagent systems under dynamically changing interaction topologies , 2005, IEEE Transactions on Automatic Control.

[19]  Jie Lin,et al.  Coordination of groups of mobile autonomous agents using nearest neighbor rules , 2003, IEEE Trans. Autom. Control..

[20]  J.N. Tsitsiklis,et al.  Convergence in Multiagent Coordination, Consensus, and Flocking , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[21]  P. Hall,et al.  Martingale Limit Theory and its Application. , 1984 .

[22]  Soummya Kar,et al.  Distributed Average Consensus in Sensor Networks with Random Link Failures and Communication Channel Noise , 2007, 2007 Conference Record of the Forty-First Asilomar Conference on Signals, Systems and Computers.

[23]  V. Borkar,et al.  Asymptotic agreement in distributed estimation , 1982 .

[24]  Dario Bauso,et al.  Consensus for switched networks with unknown but bounded disturbances , 2006 .

[25]  P. Graefe Linear stochastic systems , 1966 .

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

[27]  Jonathan H. Manton,et al.  Coordination and Consensus of Networked Agents with Noisy Measurements: Stochastic Algorithms and Asymptotic Behavior , 2009, SIAM J. Control. Optim..

[28]  Ruggero Carli,et al.  Communication constraints in the average consensus problem , 2008, Autom..

[29]  Han-Fu Chen Stochastic approximation and its applications , 2002 .

[30]  Stephen P. Boyd,et al.  Distributed average consensus with least-mean-square deviation , 2007, J. Parallel Distributed Comput..

[31]  Amr El Abbadi,et al.  Distributed average consensus with stochastic communication failures , 2007, 2007 46th IEEE Conference on Decision and Control.

[32]  Sonia Martínez,et al.  Robust rendezvous for mobile autonomous agents via proximity graphs in arbitrary dimensions , 2006, IEEE Transactions on Automatic Control.

[33]  Sanjeev R. Kulkarni,et al.  Noise Conditions for Prespecified Convergence Rates of Stochastic Approximation Algorithms , 1999, IEEE Trans. Inf. Theory.

[34]  Valerie Isham,et al.  Non‐Negative Matrices and Markov Chains , 1983 .

[35]  Richard M. Murray,et al.  Consensus problems in networks of agents with switching topology and time-delays , 2004, IEEE Transactions on Automatic Control.

[36]  P. Hall,et al.  Martingale Limit Theory and Its Application , 1980 .

[37]  Chai Wah Wu,et al.  Synchronization and convergence of linear dynamics in random directed networks , 2006, IEEE Transactions on Automatic Control.