Adaptive synchronization of uncertain underactuated Euler-Lagrange agents

This work proposes a framework for adaptive synchronization of uncertain underactuated Euler-Lagrange (EL) agents. The designed distributed controller can handle both state-dependent uncertain system dynamics terms and state-dependent uncertain interconnection terms among neighboring agents. No structural knowledge of such terms is required other than the standard properties of EL systems (positive definite mass matrix, bounded gravity, velocity-dependent friction bound, etc.). The study of stability relies on a suitable analysis of the non-actuated and the actuated synchronization errors, resulting in stable error dynamics perturbed by parametrized state-dependent uncertainty. This uncertainty is tackled via appropriate adaptation laws, giving stability in the uniform ultimate boundedness sense, in line with the available literature on state-dependent uncertain system dynamics and/or state-dependent uncertain interconnections. An example with a network of boom cranes is used to validate the proposed approach.