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

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.