A finite-time adaptive order estimation approach for non-integer order nonlinear systems

This paper proposes some methods for estimating the order of nonlinear systems having non-integer order. First, the stability of time-varying order systems is studied. Afterward, the multivariable systems with time-varying incommensurate order are studied and an estimation scheme is proposed to approximate the order. In the next step, considering the pseudo-states of a system to be unknown, an order/pseudo-state estimator is designed for a category of nonlinear systems. It is shown that the method is extendible to form order/pseudo-state estimators for other classes of nonlinear systems using other traditional nonlinear observers. One of the advantages of the proposed methods is that a compact time interval is enough to guarantee bounded estimation error. (C) 2021 ISA. Published by Elsevier Ltd. All rights reserved.