Distributed optimal coordination for multiple heterogeneous Euler-Lagrangian systems

In this paper, we consider the distributed optimal coordination (DOC) problem for multi-agent systems with the agents in the form of Euler-Lagrangian (EL) dynamics. We propose two different distributed protocols for the heterogeneous continuous-time EL agents to achieve the optimization task. By constructing suitable Lyapunov functions, we prove the global convergence to the optimal coordination of the EL systems in the case with parametric uncertainties, and the global exponential convergence in the case without parametric uncertainties. Furthermore, we estimate the regret bound for an uncertain DOC problem with time-varying cost functions and inexact gradients. Finally, we provide a numerical example to validate the theoretical results.