Synchronization of Networked Lagrangian Systems

In this paper we study the problem of synchronization of networked Lagrangian systems. This problem arises in applications such as the control of multiple robots, formation control of UAV’s, mobile sensor networks, Kuramoto oscillators, and teleoperation. We assume that the agents exchange position and velocity information over a network described by an interconnection graph. We consider only linear interconnections on balanced, directed graphs but similar results can also be derived for nonlinear interconnections on undirected graphs. Our results exploit the well-known passivity property of Lagrangian mechanical systems. We demonstrate synchronization on both fixed and switching graphs. In the case of fixed graphs, the passivity property allows us, in addition, to treat the practically important problem of time delay in communication.

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