Jun Yang

TL;DR: The stability of the closed-loop control system, including the unknown dynamics estimator and the feedback control is proved, and an alternative, simple approximation-free control method for pure-feedback systems, where only the system output needs to be measured.

Abstract: This paper provides a modified model reference adaptive control (MRAC) scheme to achieve better transient control performance for systems with unknown unmatched dynamics, where an adaptive law with guaranteed convergence is introduced. We first revisit the standard MRAC system and analyze the tracking error bound by using L2‐norm and Cauchy‐Schwartz inequality. Based on this analysis, we suggest a feasible way to compensate the undesired transient dynamics induced by the gradient descent–based adaptive laws subject to sluggish convergence or even parameter drift. Then, a modified adaptive law with an alternative leakage term containing the parameter estimation error is developed. With this adaptive law, the convergence of both the estimation error and tracking error can be proved simultaneously. This enhanced convergence property can contribute to deriving smoother control signal and improved control response. Moreover, this paper provides a simple and numerically feasible approach to online verify the well‐known persistent excitation condition by testing the positive definiteness of an introduced auxiliary matrix. Comparative simulations based on a benchmark 3‐DOF helicopter model are given to validate the effectiveness of the proposed MRAC approach and show the improved performance over several other MRAC schemes.

TL;DR: A new adaptive algorithm with the extracted NN weights error is incorporated into adaptive control, where a novel leakage term is superimposed on the gradient method and the convergence of both the tracking error and the estimation error can be guaranteed simultaneously.