Synchronization of Chaotic Systems Using Time-Delayed Fuzzy State-Feedback Controller

Abstract

Abstract-This paper presents the fuzzy-model-based control approach to synchronize two chaotic systems subject to parameter uncertainties. A fuzzy state-feedback controller using the system state of response chaotic system and the time-delayed system state of drive chaotic system is employed to realize the synchronization. The time delay which complicates the system dynamics makes the analysis difficult. To investigate the system stability and facilitate the design of fuzzy controller, T-S fuzzy models are employed to represent the system dynamics of the chaotic systems. Furthermore, the membership grades of the T-S fuzzy models become uncertain due to the existence of parameter uncertainties which further complicates the system analysis. To ease the stability analysis and produce less conservative analysis result, the membership functions of both T-S fuzzy models and fuzzy controller are considered. Stability conditions are derived using Lyapunov-based approach to aid the design of fuzzy state-feedback controller to synchronize the chaotic systems. Simulation examples are presented to illustrate the merits of the proposed approach.

Asynchronous Piecewise Output-Feedback Control for Large-Scale Fuzzy Systems via Distributed Event-Triggering Schemes

“…and all notations are defined in (32). By introducing the positive scalars ϵ i , and using Lemma A2 in Appendix, the inequality in (31) is obtained, which completes the proof.…”

“…In [31], further extensions to uncertain grades of membership were presented, and the less conservative results were derived by relaxing some restrictive conditions. In [32], the asynchronous grades of membership were considered as disturbances, and the design of fuzzy statefeedback controller to synchronize the chaotic systems was derived in the form of LMIs. The work in [33] reconstructed the synchronous grades of membership between the controller and the plant under communication network, two relaxing criteria to stability analysis and controller synthesis were derived.…”

Application of Advanced Encryption Standard to Chaotic Synchronization Systems: Using an Improved Genetic Algorithm as Auxiliary

“…Synchronization of two identical chaotic oscillators called transmitter (master) and receiver (slave) is required in chaos secure communications. Consequently, chaotic synchronization has become a common study [4]. However, most synchronization methods are focused on synchronizing two identical chaotic systems with different initial conditions [5].…”

New criteria on delayed state feedback stabilization for stochastic systems with time-varying delay

“…The problems of stabilization for deterministic systems with input delay were intensively studied (see [9][10][11][12][13]) over the past few years. The delayed state feedback approach was also used to stabilize the periodic motions of an oscillator or chaotic system (see [14][15][16]). However, there are few papers concerning with the stochastic systems with input delay [3,17,18].…”