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Feedback control and adaptive control of the energy resource chaotic system. (English) Zbl 1129.93403
Summary: The problem of control for the energy resource chaotic system is considered. Two different method of control, feedback control (include linear feedback control, non-autonomous feedback control) and adaptive control methods are used to suppress chaos to unstable equilibrium or unstable periodic orbits. The Routh-Hurwitz criteria and Lyapunov direct method are used to study the conditions of the asymptotic stability of the steady states of the controlled system. The designed adaptive controller is robust with respect to a certain class of disturbances in the energy resource chaotic system. Numerical simulations are presented to show these results.

##### MSC:
 93B52 Feedback control 37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior 37N25 Dynamical systems in biology 92B20 Neural networks for/in biological studies, artificial life and related topics 93C40 Adaptive control/observation systems 93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, $$L^p, l^p$$, etc.) in control theory 93D20 Asymptotic stability in control theory
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