Stabilisation of unknown fractional‐order chaotic systems: an adaptive switching control strategy with application to power systems

Abstract

In this study, a switching adaptive controller is introduced to stabilise fractional-order dynamical systems with completely unknown dynamics and structure. The boundedness property of the chaotic systems is used to design a switching adaptive control scheme which suppresses the chaotic behaviour of the fractional-order systems. The analytical terms of this approach are proved based on the stability analysis theorem of the fractional-order systems and the adaptive control method. Robust stability and simplicity in design are some interesting capabilities of the designed scheme. The proposed method is a general one in which it can overcome the system's unknown parameters and uncertainties. In addition, the proposed adaptive approach is applied for control of a class of three-dimensional fractional-order systems via a single control input. Some illustrative examples, including an application to stabilisation of a chaotic model of a power system, are given to show the efficacy of the proposed adaptive approaches.