Switched MRAC with improved performance using Semi-Initial Excitation

摘要

This work generalizes the recently developed initial excitation (IE) based adaptive control by introducing the notion of semi-initial excitation (semi-IE), a still relaxed version of IE. Typically, classical adaptive controllers guarantee Lyapunov stability of the overall error dynamics (tracking error + parameter estimation error) and asymptotic convergence of tracking error to zero, while requiring a restrictive condition of persistence of excitation (PE) for parameter convergence. The authors' recent work on a new adaptive control architecture based on the milder IE condition guarantees parameter convergence while ensuring exponential stability of the overall error dynamics once the online verifiable IE condition is satisfied. The current work further relaxes the excitation condition by proposing the concept of semi-IE. The proposed adaptive controller is proved to guarantee convergence of the parameter estimation error to a lower dimensional manifold under the weaker semi-IE condition, while the stronger condition of IE guarantees convergence of the parameter estimation error to zero. The designed adaptive algorithm has been shown to significantly improve the transient response of tracking error as compared to the conventional approaches.