Direct adaptive tuning of robust controllers with guaranteed stability properties

We address the following problem: given a fixed regulator that insures closed-loop stability for a partially known plant, design a mechanism to adaptively tune the controller parameters in order to improve performance. Our main concern is to insure that global _∞-stability of the overall system is preserved. The proposed parameter update law includes a signal normalization [1] and a σ-modification [2]. The condition for global _∞-stability relates the margin of stability of the closed-loop linear system, the speed of adaptation and the size of the residual set for the tracking error.