A class of adaptive predefined-time extended state observers for high-order strict-feedback systems

Fast state estimation for nonlinear systems has been a key issue in control theory and the recently developed predefined-time stability acts as an effective tool for the problem. However, the studies of predefined-time state observer for nonlinear systems are rare. In this article, we consider the predefined-time extended state observer (PTESO) design for a class of high-order strict-feedback systems subject to Hölder continuous nonlinearities and lumped disturbance. By developing an adaptive mechanism and using time-varying functions, a class of adaptive PTESOs is designed to estimate the unavailable states and the lumped disturbance, in which the convergence time can be tightly and explicitly preset by only one parameter, irrelevant to the initial conditions. The adaptive mechanism is used to improve the transient performance under wide-range lumped disturbance. Moreover, thanks to the design of the time-varying gains, the PTESO could realize fast observation with trivial peaking observation errors. Finally, simulation results are provided to illustrate the effectiveness of the proposed observer.