A Novel Continuous Finite-Time Extended State Observer Design for a Class of Uncertain Nonlinear Systems

In this paper, an innovative technique to design a finite-time extended state observer (FT-ESO) for a class of nonlinear systems is proposed. This FT-ESO aims to estimate the full state of a nonlinear system as well as the uncertainties and/or disturbances in a finite time. First, the nonlinear model of the system is transformed into the normal form using a diffeomorphism map. Then, as the main innovation of this paper, the nonlinear system is transformed into a new time-varying form to achieve the finite-time boundedness criteria of the estimation error variables using the asymptotic stability methods. Next, without any prior knowledge about the upper bounds of the uncertainties and/or disturbances, and only based on the output measurements, the FT-ESO is designed. In this approach, the time-varying gains of the extended state observer are designed to converge the observation error to a neighborhood of zero while remaining uniformly bounded in finite-time. Finally, the efficiency of the proposed FT-ESO for classes of uncertain nonlinear systems with unknown measurement noise is illustrated by numerical simulations.