Abstract:
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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. |