Performance improvement in adaptive control

The FT identification method has two distinguishing features. First, the true parameter estimate is obtained at any time instant the excitation condition is satisfied, and second, the procedure allows for a direct and immediate removal of any perturbation signal injected into the closed-loop system to aid in parameter estimation. However, the drawback of the FT identification algorithm is the requirement to check the invertibility of a matrix online and compute the inverse matrix when appropriate. To avoid these concerns and enhance the applicability of the FT method in practical situations, the procedure is hereby exploited to develop a novel adaptive compensator that (almost) recovers the performance of the FTI. The compensator guarantees exponential convergence of the parameter estimation error at a rate dictated by the closed-loop system's excitation. It was shown how the adaptive compensator can be used to improve upon existing adaptive controllers. The modification proposed guarantees exponential stability of the parametric equilibrium provided the given PE condition is satisfied. Otherwise, the original system's closed-loop properties are preserved.