Robustness of the combined model reference adaptive control

This paper analyzes the robustness of combined model reference adaptive control. The methods presented here use a combined model reference adaptive control method developed for the ideal case together with four types of modifications of the adaptive laws. A dead zone type of modification, the knowledge of a bound on the norm of the desired controller parameter vector, and the so-called σθ and |e|θ modifications are introduced in the controller as well as the identifier adaptive laws. With these modifications, the resultant algorithms are robust in the presence of bounded external perturbations. Global stability of the overall adaptive systems is demonstrated in all four cases. Stability proof is accomplished by using the Lyapunov theory and some of its extensions. With the proposed method, it is possible to improve the transient behavior of the resultant adaptive systems.