Fuzzy Synchronization of Chaotic Systems with Hidden Attractors

Abstract

Chaotic systems are hard to synchronize, and no general solution exists. The presence of hidden attractors makes finding a solution particularly elusive. Successful synchronization critically depends on the control strategy, which must be carefully chosen considering system features such as the presence of hidden attractors. We studied the feasibility of fuzzy control for synchronizing chaotic systems with hidden attractors and employed a special numerical integration method that takes advantage of the oscillatory characteristic of chaotic systems. We hypothesized that fuzzy synchronization and the chosen numerical integration method can successfully deal with this case of synchronization. We tested two synchronization schemes: complete synchronization, which leverages linearization, and projective synchronization, capitalizing on parallel distributed compensation (PDC). We applied the proposal to a set of known chaotic systems of integer order with hidden attractors. Our results indicated that fuzzy control strategies combined with the special numerical integration method are effective tools to synchronize chaotic systems with hidden attractors. In addition, for projective synchronization, we propose a new strategy to optimize error convergence. Furthermore, we tested and compared different Takagi–Sugeno (T–S) fuzzy models obtained by tensor product (TP) model transformation. We found an effect of the fuzzy model of the chaotic system on the synchronization performance.

Cifrado de texto mediante atractores caóticos: CRYPTOGUARD

“…Después, la información cifrada es enviada a través de un canal para ser recibida por el receptor. Finalmente, el receptor utiliza la sincronización para recuperar el mensaje original de la información cifrada [7].…”

On the Analysis of Regularized Fuzzy Systems of Uncertain Differential Equations

“…Several books and articles that summarized important results of the theory of fuzzy differential equations and their applications in electricity, mechanics, physics, engineering, biology, and economics have been indicated by the authors in [2] (see, for example, Refs. [3][4][5][6][7][8][9][10][11][12][13][14][15][16] and the references therein). Also, the notion of fuzzy entropy in the framework of fuzzy functions has recently engaged research interests [17,18].…”

Fixed-Time Adaptive Chaotic Control for Permanent Magnet Synchronous Motor Subject to Unknown Parameters and Perturbations

“…backstepping control [7][8][9][10][11][12][13][14], sliding mode control [15][16][17][18][19][20][21][22], iterative learning control [23], and intelligent control [24][25][26][27][28][29][30][31][32][33][34][35].…”