Minimum communication cost consensus in multi-agent systems with Markov chain patterns

The authors study the problem of optimising the communication cost for multi-agent systems over both undirected topology and directed topology. The authors assume that the two adjacent agents exchange information with a certain probability. Necessary and sufficient conditions for multi-agent systems to achieve the mean square consensus are obtained by using the matrix and graph theories. In particular, the authors formulate a definition of the communication cost function and propose the methods to minimise the proposed cost function. Simulation examples are also given to illustrate the theoretical results.