Synchronization of Chaos Systems Using Fuzzy Logic

Abstract

Problem statement: This study presented a new and systematic method to robustly synchronize uncertain chaos systems. It was derived based on the observer approach for synchronization, where error dynamics was made asymptotically stable around the zero to accomplish synchronization. Approach: This method viewed the synchronization problem as a control problem in order to make use of the literature available in this field. In addition, it consisted of designing a digital response system to synchronize with a given continuous-time chaotic drive system. Takagi-Sugeno (TS) fuzzy model was used to model the chaotic dynamic system, while the uncertainties were decomposed such that the uncertain chaotic system could be rewritten as a set of local linear models with an additional disturbed input. Results: This study demonstrated the effectiveness of the methodology presented. The response (receiver) system was able to synchronize very closely with drive (transmitter) system. Furthermore, both piecewise linear and nonlinear uncertain Chua circuits synchronized wonderfully with insignificant errors. Conclusion: The study confirmed that it is capable of achieving excellent synchronization performances, even in the presence of significant parametric uncertainties for uncertain chaos systems. The Takagi-Sugeno (TS) fuzzy model was used to model the chaotic dynamic system, while the uncertainties are decomposed such that the uncertain chaotic system was rewritten as a set of local linear models with an additional disturbed input.