Almost sure convergence to consensus in Markovian random graphs

— In this paper we discuss the consensus problem for a network of dynamic agents with undirected information flow and random switching topologies. The switching is determined by a Markov chain, each topology corresponding to a state of the Markov chain. We show that in order to achieve consensus almost surely and from any initial state the sets of graphs corresponding to the closed positive recurrent sets of the Markov chain must be jointly connected. The analysis relies on tools from matrix theory, Markovian jump linear systems theory and random processes theory. The distinctive feature of this work is addressing the consensus problem with “Markovian switching” topologies.

• Type: Conference
• Year: 2008
• Where: CDC
• Authors: Ion Matei, Nuno C. Martins, John S. Baras
• Keywords: CDC 2008, Consensus Problem, Control Systems, Markov Chain, Random Switching Topologies