A Finite-time Sliding Mode Observer for a Class of Perturbed Nonholonomic Systems

Abstract

In this paper, an equivalent output injection based sliding mode observer is proposed for estimating the states of a class of perturbed n-dimensional nonholonomic systems. In the proposed design, we introduce a new transformation based on state scaling which renders the perturbed system in a triangular input form, amenable for the design of the observer. Thereafter, the equivalent control method is adopted in a sequential manner to estimate each of the system states one after another, in finite time such that ultimately all the states are estimated. Thus the entire state estimates are available for feedback after a finite time, in the presence of structured perturbations affecting the system. Simulations are performed on a unicycle mobile robot, to demonstrate the effectiveness of the proposed observer design.