Robust synchronization of arrays of Lagrangian systems

Abstract

A new technique to synchronize arrays of uncertain, disturbed Lagrangian systems, where the synchronization signals use only the position measurement, is proposed. The technique, robust with respect to some kinds of connection losses and matched disturbances, can be applied to different topologies whose connection matrix is not necessarily symmetric. The design of the coupling signals is based on a discontinuous robust observer that identifies, at the same time, the velocity vector and any matched disturbance containing unknown terms, parameter uncertainty, or unknown external perturbations. This estimated disturbance is incorporated in the coupling signal to compensate the real perturbations, improving significantly the synchronization performance. The technique is illustrated with numerical simulations and some experiments carried on some real systems.