Uncertain Fractional Order Chaotic Systems Tracking Design via Adaptive Hybrid Fuzzy Sliding Mode Control

Abstract

In this paper, in order to achieve tracking performance of uncertain fractional order chaotic systems an adaptive hybrid fuzzy controller is proposed. During the design procedure, a hybrid learning algorithm combining sliding mode control and Lyapunov stability criterion is adopted to tune the free parameters on line by output feedback control law and adaptive law. A weighting factor, which can be adjusted by the trade-off between plant knowledge and control knowledge, is adopted to sum together the control efforts from indirect adaptive fuzzy controller and direct adaptive fuzzy controller. To confirm effectiveness of the proposed control scheme, the fractional order chaotic response system is fully illustrated to track the trajectory generated from the fractional order chaotic drive system. The numerical results show that tracking error and control effort can be made smaller and the proposed hybrid intelligent control structure is more flexible during the design process.

Adaptive type‐2 fuzzy system for synchronisation and stabilisation of chaotic non‐linear fractional order systems

“…In recent years, adaptive fuzzy systems have been applied to control non-linear fractional order systems. Lin et al have introduced an adaptive indirect fuzzy sliding mode for synchronisation of the uncertain chaotic fractional order systems [47][48][49]. Likewise, Lin and Lee [4] have proposed an adaptive fuzzy sliding mode to synchronise the uncertain chaotic fractional order time-delay systems.…”