Global optimal consensus for multi-agent systems with bounded controls

Abstract

This paper studies the global optimal consensus problem for a multi-agent system with bounded controls. Each agent has its own objective function which is known only to itself. We focus on two multi-agent systems, the single integrator multi-agent system and the double-integrator multi-agent system. For each of these two multi-agent systems, we construct, for each agent, a bounded local control protocol that uses the information accessible to it through the communication topology underlying the multi-agent system and information of its own objective function. It is shown that these control protocols together achieve global optimal consensus for the multi-agent system, that is, all agents reaching consensus at a state that minimizes the sum of the objective functions of all agents as long as the communication topology is strongly connected and detailed balanced. Simulation results are given to illustrate the theoretical results.