Adaptive regulation of a class of uncertain nonlinear systems by output feedback

This paper studies the problem of global stabilization by output feedback for a family of uncertain nonlinear systems without zero dynamics. The class of uncertain systems under consideration is assumed to be dominated by a bounding system, which is of polynomial growth in the unmeasurable states and can be a polynomial function of the system output, with unknown growth rate. To achieve global state regulation in the presence of parametric uncertainty, we propose a non-identifier based output feedback control scheme by employing the idea of universal control integrated with the design of a linear high-gain observer, whose gains are composed of two components, both of them are not constant and need to be dynamically updated. The novelty of this paper is that a universal-type adaptive output feedback controller is numerically constructed by using a sum of squares (SOS) optimization algorithm, which can globally regulate all the states of the uncertain systems while maintaining global boundedness of the closed-loop system. An example is presented to show the effectiveness of this methodology.