Coordination of Multi-agent Systems via Energy—Shaping: Networking Improves Robustness

In this paper the problem of robust coordination of multi-agent systems via energy–shaping is studied. The agents are nonidentical, Euler-Lagrange systems with uncertain parameters. The control objective is to drive all agents states to the same constant equilibrium—which is achieved shaping their potential energy function. It is assumed that, if the parameters are known, this task can be accomplished with a decentralized strategy. In the face of parameter uncertainty, the assigned equilibrium is shifted away from its desired value. It is shown that adding information exchange between the agents to this decentralized control policy improves the performance. More precisely, it is proven that if the communication graph is undirected and connected, the equilibrium of the networked controller is always closer (in a suitable metric) to the desired one. If the the potential energy functions are quadratic, the result holds for all interconnection gains, else, it is true for sufficiently large gains. The decentralized controller is the well–known energy–shaping proportional plus derivative controller, extensively used in applications. An additional advantage of networking is that the control objective is achieved injecting lower gains into the loop.