Global optimal consensus of multi-agent systems with bounded controls

This paper studies the global optimal consensus problem for a multi-agent system with bounded controls. Each agent is described by a single-integrator dynamics and has its own objective function which is known to itself only. For each agent, we construct a bounded local control law that uses the information accessible to it through the communication topology underlying the multi-agent system. It is shown that these control laws together achieve global optimal consensus for the multi-agent system, that is, all agents reach 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 weight-balanced. Simulation results are given to illustrate the theoretical results.