Robust H∞ fuzzy control of dithered chaotic systems

In this study, a combining scheme of fuzzy controllers and dithers via NN-based approach was proposed to tame the chaotic system. In terms of Lyapunov's direct method, a stability criterion was derived to guarantee that the trajectory described by the chaotic system under fuzzy control can be steered into a periodic orbit or a steady state. According to the stability condition of this criterion, a fuzzy controller was then synthesized to control chaos and achieve the H∞ control performance at the same time. A high frequency signal (commonly referred to as dither) was simultaneously injected to quench the chaotic motion when the fuzzy controller cannot quell the chaos. Finally, a numerical example of Chua's oscillator circuit with simulations is provided to demonstrate the feasibility of our approach.