Generalized projective synchronization of uncertain chaotic systems with external disturbance |
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| Authors: | Faezeh Farivar Mahdi Aliyari Shoorehdeli Mohammad Ali Nekoui Mohammad Teshnehlab |
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| Affiliation: | 1. Laboratory of Systems Biology and Bioinformatics (LBB), Institute of Biochemistry and Biophysics, University of Tehran, Tehran, Iran;2. Department of Electrical and Computer Engineering, Khajeh-Nasir Toosi University, Tehran, Iran;3. Department of Mechatronics, Khajeh-Nasir Toosi University, Tehran, Iran;1. Faculty of Electrical Engineering, Department of Control Engineering, K. N. Toosi University of Technology, Tehran, Iran;2. Faculty of Electrical Engineering, Department of Mechatronics Engineering, K. N. Toosi University of Technology, Tehran, Iran;1. Department of Engineering Cybernetics, Norwegian University of Science and Technology, 7491 Trondheim, Norway;7. Centerfor Autonomous Marine Operations and Systems, Department of Engineering Cybernetics, Norwegian University of Science and Technology, 7491 Trondheim, Norway;71. Kelda Drilling Controls |
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| Abstract: | This paper proposes the generalized projective synchronization (GPS) of uncertain chaotic systems with external disturbance via Gaussian radial basis adaptive sliding mode control (GRBASMC). A sliding surface is adopted to ensure the stability of the error dynamics in sliding mode control. In the neural sliding mode controller, a Gaussian radial basis function is utilized to online estimate the system dynamic function. The adaptation law of the control system is derived in the sense of Lyapunov function, thus the system can be guaranteed to be asymptotically stable.The proposed method allows us to arbitrarily adjust the desired scaling by controlling the slave system. It is not necessary to calculate the Lyapunov exponents and the eigen values of the Jacobian matrix, which makes it simple and convenient. Also, it is a systematic procedure for GPS of chaotic systems and it can be applied to a variety of chaotic systems no matter whether it contains external excitation or not. Note that it needs only one controller to realize GPS no matter how much dimensions the chaotic system contains and the controller is easy to be implemented.The proposed method is applied to three chaotic systems: Genesio system, Lur’e like system and Duffing system. |
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