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On control and synchronization in chaotic and hyperchaotic systems via linear feedback control. (English) Zbl 1221.93230
Summary: We present the control and synchronization of chaos by designing linear feedback controllers. The linear feedback control problem for nonlinear systems is 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.
MSC:
93D15Stabilization of systems by feedback
37D45Strange attractors, chaotic dynamics
34H10Chaos control (ODE)
49N10Linear-quadratic optimal control problems
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