Abstract
In this paper, a robust adaptive type-2 fuzzy higher order sliding mode controller is designed to stabilize the unstable periodic orbits of uncertain perturbed chaotic system with internal parameter uncertainties and external disturbances. In Higher Order Sliding Mode Control (HOSMC),the chattering phenomena of the control effort is reduced, by using Super Twisting algorithm. Adaptive interval type-2 fuzzy systems are proposed to approximate the unknown part of uncertain chaotic system and to generate the Super Twisting signals. Based on Lyapunov criterion, adaptation laws are derived and the closed loop system stability is guaranteed. An illustrative example is given to demonstrate the effectiveness of the proposed controller.
Highlights
Chaotic phenomenon is widely observed in several applications such as: medical field, fractal theory, electrical circuits and secure communication [1]
Adaptive interval type-2 fuzzy systems are proposed to approximate the unknown part of uncertain chaotic system and to generate the Super Twisting signals
Many nonlinear control techniques have been successfully applied on chaos control and synchronization of different dynamical systems [3,4,5], nonlinear control [6,7], active control and backstepping design [8,9,10], fuzzy logic and adaptive control [11,12], adaptive fuzzy control [13]
Summary
Chaotic phenomenon is widely observed in several applications such as: medical field, fractal theory, electrical circuits and secure communication [1]. The High Order Sliding Mode Control (HOSMC) has been presented to reduce and (or) remove the chattering phenomenon This technique provides higher accuracy than the standardSMC [21,22,23]. A higher order sliding mode controlcombined with adaptive type-2 fuzzy systems, is proposed to design a robust controller for stabilization of unknown SISO nonlinear chaotic system, working in the presence of uncertainties and external disturbances. We introduced adaptive type-2 fuzzy systems for model the unknown dynamic of system and simplify the calculation of gains in the second order sliding mode. Their updates are performed using adaptation laws derived from the stability studyin the Lyapunov sense.
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