A Distributed Consensus Algorithm via LMI-Based Model Predictive Control and Primal-Dual Decomposition

This paper deals with an output consensus problem of multiple agents and first presents a centralized algorithm for solving it by a model predictive control method based on linear matrix inequalities. It is shown that the outputs of all the agents controlled by the presented method asymptotically converge to a common point, i.e., a consensus point. Then two kinds of algorithms for solving the consensus problem in a decentralized way are presented by using primal and dual decomposition methods. In general, these algorithms require a large number of iterations, i.e., a large number of communications between agents. To cope with this communication burden, a method that can reduce the number of iterations and guarantee the convergence to a consensus point is proposed by exploiting the property that the primal and dual decomposition methods can give upper and lower bounds of the optimal value of the optimization problem to be solved. A numerical example is given to illustrate the effectiveness of the proposed method.