The design of a new hybrid controller for fractional-order uncertain chaotic systems with unknown time-varying delays

Abstract

In this paper, the combination of a soft computing technique, i.e., adaptive neuro-fuzzy inference system (ANFIS) with fractional-order robust adaptive control is used to control a class of fractional order uncertain chaotic nonlinear systems with uncertainty, external disturbances and unknown time-varying delays. At first, the fractional-order hyperbolic tangential robust adaptive intelligent controller (FHRAIC) is designed for the system, when the unknown time-varying heterogeneous delays and uncertainties and disturbances exist in system states. Next, the controller design is extended for the case of existence of unknown time-varying delay in the inputs of the system. The hyperbolic tangential sliding surface enables the closed-loop system to safely and effectively avoid large errors in tracking control. Adaptive control parameters are adjusted based on Lyapunov stability analysis ANFIS is used to approximate unknown functions. The stability analysis of this controller has been carried out based on Lyapunov–Krasovskii method and Barbalat’s Lemma. Various simulation examples show the effectiveness of the proposed method for a vast range of systems. To demonstrate the effectiveness of ANFIS on FHRAIC controller, its performance has been compared with that of fractional-order hyperbolic tangential robust adaptive controller (FHRAC).