On control and synchronization in chaotic and hyperchaotic systems via linear feedback control |
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Affiliation: | 1. Department of Mathematics, Faculty of Science Bilkent University, Ankara 06800, Turkey;2. Department of Mathematics, Faculty of Science Hacettepe University, Ankara 06800, Turkey |
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Abstract: | This paper presents the control and synchronization of chaos by designing linear feedback controllers. The linear feedback control problem for nonlinear systems has been formulated under optimal control theory viewpoint. Asymptotic stability of the closed-loop nonlinear system is guaranteed by means of a Lyapunov function which can clearly be seen to be the solution of the Hamilton–Jacobi–Bellman equation thus guaranteeing both stability and optimality. The formulated theorem expresses explicitly the form of minimized functional and gives the sufficient conditions that allow using the linear feedback control for nonlinear system. The numerical simulations were provided in order to show the effectiveness of this method for the control of the chaotic Rössler system and synchronization of the hyperchaotic Rössler system. |
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