Fuzzy control of dithered chaotic systems via neural-network-based approach

This paper presents an effective approach for controlling chaos. First, a neural-network (NN) model is employed to approximate the chaotic system. Then, a linear differential inclusion (LDI) state-space representation is established for the dynamics of an NN model. Based on the LDI state-space representation, a fuzzy controller is proposed to tame the chaotic system. If the designed fuzzy controller cannot suppress the chaos, a high frequency signal, commonly called dithers, is simultaneously injected into the chaotic system. According to the relaxed method, an appropriate dither is introduced to steer the chaotic motion into a periodic orbit or a steady state. If the frequency of dither is high enough, the trajectory described by the dithered chaotic system and that of its corresponding mathematical model-the relaxed system can be made as close as desired. This phenomenon enables us to get a rigorous prediction of the dithered chaotic system's behavior by obtaining the behavior of the relaxed system. Finally, a numerical example with simulations is given to illustrate the concepts discussed throughout this paper.