ADAPTIVE NONLINEAR FEEDBACK DESIGN FOR CHAOS SUPPRESSION AND REGULATION IN UNCERTAIN UNIFIED CHAOTIC SYSTEM

作者：Ataei M^*; Haghighatdar F

来源：International Journal of Innovative Computing Information and Control, 2011, 7(5A): 2051-2062.

• Adaptive control
• Unified chaotic system
• Lyapunov's stability theory
• Chaos suppression
• Regulation

In this paper, an adaptive method for chaos suppression and regulation in uncertain unified chaotic system is proposed. For this purpose, at the first step, an adaptive non-linear state feedback is designed to suppress the chaotic behavior of under consideration system. In this way, the Lyapunov's direct method is used to select the appropriate adaptive non-linear state feedback. The asymptotic stability guarantee of uncertain unified chaotic system using non-linear feedback controller, in a stochastic point on the general manifold of its equilibrium points, is proved in a lemma. At the second step, a combination of suggested adaptive non-linear state feedback and linear feedbacks, with constant and adaptive gains, is used to regulate the controlled system at the desired set-point placed on the general related equilibrium manifold. In this stage, the asymptotic stability of the controlled system on the desired set-point is proved in another lemma using the Lyapunov's indirect method. Finally, simulation results of applying the controllers to uncertain unified chaotic system for different cases are provided to show the well-acceptable performance of the proposed controllers.

• 出版日期2011-5