Adaptive synchronization of two chaotic systems with stochastic unknown parameters |
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| Authors: | Hassan Salarieh Aria Alasty |
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| Affiliation: | 1. Department of Electrical and Computer Engineering, Hakim Sabzevari University, Sabzevar, Iran;2. Department of Mathematics, Faculty of Arts and Sciences, Cankaya University, 06530 Ankara, Turkey;3. Institute of Space Sciences, P.O.Box, MG-23, R 76900, Magurele-Bucharest, Romania;4. Department of Electrical Engineering, University of Bojnord, P.O. Box, 94531-1339, Bojnord, Iran;1. Laboratoire Robotique, Informatique et Systèmes Complexes (RISC, LR16ES07), Ecole Nationale d’Ingénieurs de Tunis, Université de Tunis El Manar, BP. 37, Le Belvédère, 1002 Tunis, Tunisia;2. Institut Supérieur des Technologies de l’Information et de la Communication, Université de Carthage, Borj Cedria 1164, Tunis, Tunisia;1. Department of Electrical Engineering, University of Bojnord, P.O. Box 94531-1339, Bojnord, Iran;2. Department of Mathematics, Sahand University of Technology, P.O. Box 51335-1996, Tabriz, Iran;3. Department of Mathematics, Faculty of Arts and Sciences, Cankaya University, 06530 Ankara, Turkey;4. Institute of Space Sciences, P.O. Box MG-23, 76900, Magurele, Bucharest, Romania;1. Department of Mechanical Engineering, Amirkabir University of Technology, Tehran 15875, Iran;2. Department of Mechanical Engineering, Sharif University of Technology, Tehran 14588, Iran |
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| Abstract: | Using the Lyapunov stability theory an adaptive control is proposed for chaos synchronization between two different systems which have stochastically time varying unknown coefficients. The stochastic variations of the coefficients about their unknown mean values are modeled through white Gaussian noise produced by the Weiner process. It is shown that using the proposed adaptive control the mean square of synchronization error converges to an arbitrarily small bound around zero. To demonstrate the effectiveness of the proposed technique, it is applied to the Lorenz–Chen and the Chen–Rossler dynamical systems, as some case studies. Simulation results indicate that the proposed adaptive controller has a high performance in synchronization of chaotic systems in noisy environment. |
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