ROBUST STATE ESTIMATION VIA TWISTING OBSERVER

Abstract

This thesis proposes a twisting observer for state estimation of a second-order uncertain system. The observer is designed based on the twisting algorithm, a popular and simple second-order sliding mode algorithm. It relies on direct access to sign information of both the plant states, which limits its applicability to state estimation problems due to the unavailability of all states. To overcome this limitation, we propose a novel approach where the unknown sign term in the twisting observer is approximated using a delayed output-based switching function. It is shown that under some suitable gain conditions, the twisting observer guarantees arbitrary accuracy of estimation error. This can be achieved by adjusting the delay, possibly online, without affecting the system performance. The important advantage of the proposed observer is that it requires control of only the delayed term instead of nonlinear functions found in other methods that can adversely affect performance. The thesis also explores the application of the twisting observer to output feedback stabilization. The separation principle is demonstrated by independently designing the controller and observer gains for the closed-loop system.