A New Type-3 Fuzzy Logic Approach for Chaotic Systems: Robust Learning Algorithm

Abstract

The chaotic systems have extensive applications in various branches of engineering problems such as financial problems, image processing, secure communications, and medical problems, among many others. In most applications, a synchronization needs to be made with another favorite chaotic system, or output trajectories track the desired signal. The dynamics of these systems are complicated, they are very sensitive to the initial conditions, and they exhibit a stochastic unpredictable behavior. In this study, a new robust type-3 fuzzy logic control (T3-FLC) is designed that can be applied for a large case of chaotic systems under faulty actuators and unknown perturbed dynamics. The dynamic uncertainties are estimated by the online learned type-3 fuzzy logic systems (T3-FLSs). The rules of T3-FLS are optimized by the Lyapunov theorem. The actuator nonlinearities are identified by a new method. The effects of approximation error (AE), dynamic perturbations and unknown time-varying control gains are tackled by the designed adaptive compensator. The designed compensator is constructed by online estimation of the upper bound of AE. By several simulations and comparison with the new FLS-based controllers, the better performance of the designed T3-FLC is shown. In addition, the performance of the designed controller is examined in a secure communication system.

Keywords

• type-3 fuzzy control
• faulty actuator
• online-learning
• chaotic systems
• perturbed dynamics