Robust state estimation via twisting observer

Abstract

In this paper, we propose the twisting observer for robustly estimating the states of a second-order uncertain system. It is well-known that the twisting algorithm achieves the second-order sliding mode condition using the sign information of both the plant states. When all the states are not available, the twisting algorithm cannot be extended to the estimation problem directly. Hence, our proposed observer approximates this unknown sign term for the non-measurable state in the twisting observer with a delayed output-based switching function. It is shown that under some suitable gain conditions, the observer can guarantee any arbitrary accuracy of estimation error for some appropriate delay parameter which can be varied online. The advantage of this observer is that one needs to control only the delay parameter to achieve the desired steady-state accuracy, unlike the additional nonlinear functions found in the existing observers. The application of this observer to output feedback stabilization is also discussed. The separation principle for the closed-loop system is shown by designing the gains of controller and observer independently. Finally, we illustrate the design and performance of the proposed state observation scheme through a numerical example.