Neural-network based approach on delay-dependent robust stability criteria for dithered chaotic systems with multiple time-delay

Abstract

A novel approach is proposed in this study to eliminate the chaotic motion by a fuzzy controller and an appropriate dither. First, a back-propagation (BP) neural-network (NN) model is used to approximate the multiple time-delay chaotic system. Then, a linear differential inclusion (LDI) state-space representation is established for the dynamics of the NN model. Based on the LDI state-space representation, this study proposes a delay-dependent stability criterion derived in terms of Lyapunov’s direct method to guarantee that the trajectories of the multiple time-delay chaotic (MTDC) system under fuzzy control can be steered into a periodic orbit. Subsequently, the stability condition of this criterion is reformulated into a linear matrix inequality (LMI). According to the LMI, a fuzzy controller is then synthesized to tame the multiple time-delay chaotic (MTDC) system. If the fuzzy controller cannot suppress the chaos, a high frequency signal, commonly called dither, is simultaneously injected to eliminate the chaotic motion by regulating the dither’s parameters. If the frequency of dither is high enough, the trajectories of the dithered chaotic system and its corresponding mathematical model-the relaxed system can be made as close as desired. This make it possible to obtain a rigorous prediction of the dithered chaotic system’s behavior by establishing the relaxed system. Finally, this study provides a numerical example of the Chen’s chaotic system with simulations to illustrate the concepts discussed throughout this paper.