Abstract
Control of the generalized chaotic systems’ dynamical behaviors is studied here, by which a direct adaptive fuzzy controller is proposed to control a chaotic dynamical system using their Hamilton energy level. A generalized chaotic Lorenz system with hidden attractors is used as the under-control system, and its Hamilton energy is formulated and analyzed. As a practical consideration, the system is requested to be in a specific desired energy level in each explicit situation. A model-based control is computed and an adaptive fuzzy control is proposed based on it to improve the control signal from the magnitude and smoothness points of view. Adaptation law is designed to adjust the fuzzy controller parameters optimally, based on the Lyapunov second law, and guarantee the system stability. Consequent parameters of the fuzzy rules are tuned based on the residual value between the system’s Hamilton energy and the desired level. Simulation results show superiority of the proposed controller based on tracking performance and control efficiency indices.
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