Adaptive output-feedback for nonlinear systems with no a priori bounds on parameters

In a recent result [1], we proposed a dynamic high-gain observer/controller architecture for nonlinear systems of the generalized output-feedback canonical form. The design in [1] utilized the dual architecture of a high-gain observer and controller and incorporated a single dynamic scaling. The designed output-feedback controller was shown to be robust to functional and parametric uncertainties coupled with all states. However, a magnitude bound on the unknown parameters was required. In this paper, we propose a time-varying output-feedback controller that can handle time-varying nonlinear parametric uncertainty coupled with all states without requiring any a priori magnitude bounds on the unknown parameters. This is achieved using a novel time-varying dynamics of the high-gain scaling parameter. The proposed observer/controller structure provides a globally asymptotically stabilizing output-feedback solution for the benchmark open problem proposed in our earlier work with no magnitude bounds or sign information on the unknown parameter being necessary.