Parameter convergence via a novel PI-like composite adaptive controller for uncertain Euler-Lagrange systems

This work proposes a novel PI-like composite adaptive control architecture for the uncertain Euler-Lagrange (EL) systems. The composite adaptive law is strategically designed to be proportional to the parameter estimation error in addition to the tracking error, leading to parameter convergence. Unlike conventional adaptive control laws which require the regressor function to be persistently exciting (PE) for parameter convergence, the proposed method guarantees parameter convergence from a milder initially exciting (IE) condition on the regressor. The IE condition is significantly less restrictive than PE, since it does not rely on the future values of the signal and that it can be verified online. Further, the design methodology does not assume the knowledge of acceleration in the adaptive update law development. As far as the authors are aware, this is the first work on EL dynamics that achieves exponential convergence of the tracking and the parameter estimation errors to zero once the sufficient IE condition is met.