State estimations and output feedback control for nonlinear systems with cascade observers

In this paper, a new observer, namely a cascade observer, for a general class of nonlinear SISO systems is proposed. Inspired by but different from a high-gain observer, the cascade observer features a cascade structure and adaptive observer gains. In doing so the cascade observer attempts to overcome some of the typical problems that may pose to a high-gain observer. As in the case of a high-gain observer, the cascade observer structure is simple and universal in the sense that it is independent of the system dynamics and parameters. It is shown that the proposed cascade observer guarantees asymptotic stability of the estimation error. Based on the cascade observer, an adaptive output feedback controller is designed for a class of SISO nonlinear system represented globally by a nth-order differential equation. The output feedback controller has the same structure as a state feedback controller. Uniformly ultimate boundedness of tracking errors is achieved for the nonlinear systems with unknown parameters.