Composite Adaptive Control of Uncertain Euler-Lagrange Systems with Parameter Convergence without PE Condition

Abstract

This work proposes a novel composite adaptive controller for 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. The proposed adaptive controller ensures exponential convergence of the tracking and the parameter estimation errors to zero once the sufficient IE condition is met. Simulation results corroborate the efficacy of the proposed technique and also establishes it's robustness property in the presence of unmodeled bounded disturbance.