The Design of Fractional-Order Robust Adaptive Intelligent Controller for Fractional-Order Nonlinear Systems with Time Delay, Uncertainty and Disturbance

Abstract

Recently, many practical systems have been described via nonlinear fractional-order dynamic models. The design of controller for such systems is not a straightforward task, where their complex behaviors may result in chaos and bifurcation. This challenge becomes more serious when the system experiences time delays, uncertainties and disturbances. This chapter presents the controller design strategies for fractional-order nonlinear systems with time delays, uncertainties and disturbances via robust adaptive intelligent structure. Time-varying heterogeneous time delays are considered in inputs and states; and two robust adaptive intelligent strategies are designed and compared based on sliding mode and backstepping control methods. Besides, the stability analysis of the controllers is carried out based on Lyapunov-Krasovskii method and Barbalat’s Lemma. Simulation examples show the effectiveness of the proposed method for such systems. To demonstrate the effectiveness of Adaptive Network-based Fuzzy Inference System (ANFIS) on designed controller, their performance is compared with that of fractional-order robust adaptive controllers, as well.