Synchronization of networked mechanical systems without velocity information

Abstract This paper studies the synchronization problem in a network of interconnected mechanical systems where the velocity information of the interacting agents is unavailable. To achieve this, a distributed law related to the kinetic and potential energies of the considered system is proposed. Specifically, by introducing an auxiliary system and a distributed filter, it is shown that the proposed algorithm enables the synchronization of the considered system by merely using the local position measurements. Moreover, it is also shown that, compared with the existing literature, the derived synchronization conditions are irrelevant to the eigenvalues of Laplacian matrix, thus circumventing the global information of the underlying system. Moreover, on condition that the absolute position information is available, it is also shown that apart from the synchronization of agents, the discrepancy between the position variable of the original system and that of the auxiliary variable tends to zero eventually. Finally, a concrete example and some comparisons are conducted to support the formulated setup and the obtained theoretical results.