Suboptimal output consensus for a group of weakly nonminimum phase linear systems

Abstract

This paper studies the suboptimal output consensus problem for a multi-agent system, where each agent is described by a weakly nonminimum phase linear system and endowed with an objective function. For each agent, a low gain feedback based protocol consisting of a local term and a distributed term and parameterized with a low gain parameter is constructed. Under the assumption that the communication topology is strongly connected and weight-balanced, these protocols achieve suboptimal output consensus for the multi-agent system, that is, for a small enough value of the low gain parameter, the outputs of all agents reaching consensus at a value in an a priori specified arbitrarily small neighborhood of the optimal value of the overall objective function, which is the sum of the individual objective functions of all agents. The theoretical results are verified by numerical examples.