Suboptimal output consensus of a group of discrete-time heterogeneous linear non-minimum phase systems

Abstract

This paper formulates the suboptimal output consensus problem for a discrete-time heterogeneous linear multi-agent system with unstable zero dynamics, where each agent possesses its own objective function and the sum of all these private objective functions, called the overall objective function, is to be minimized. Mild assumptions on the communication topology and the agent dynamics are made under which a parameterized distributed consensus protocol based on low gain feedback is proposed for each agent. The multi-agent system is shown to achieve suboptimal output consensus under the proposed protocols in the sense that the states of all agents remain bounded while their outputs converge to a pre-specified arbitrarily small neighborhood of the optimal point as long as the design parameter is chosen small enough. Simulation results are presented that demonstrate the proposed design.