Direct adaptive tuning of robust controllers with guaranteed stability properties (Q1086536)

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 \({\mathcal L}_{\infty}\)-stability of the overall system is preserved. The proposed parameter update law includes a signal normalization and a \(\sigma\)- modification. The condition for global \({\mathcal L}_{\infty}\)-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.