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Feedback control of unknown chaotic dynamical systems based on time-series data

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3 Author(s)
Gang Chen ; Dept. of Electr. & Comput. Eng., Houston Univ., TX, USA ; Guanrong Chen ; de Figueiredo, Rui J.P.

A feedback control method is developed for controlling an unknown chaotic system, where the design is accomplished using only a finite set of one-dimensional (1-D) time-series data generated by the unknown system. The approach consists of three steps: (1) using the available time-series data to estimate a delayed time constant and an embedding dimension that both can be used to reconstruct a state space model preserving the chaotic attractor of the unknown system; (2) based on the reconstructed model, a lower order polynomial system of the same dimension is identified as a platform for controller design; and (3) a design method using the lower order approximate model is devised for determining a simple nonlinear feedback controller that works for the originally unknown underlying chaotic system. Computer simulation results on the Duffing oscillator are shown to demonstrate the effectiveness of this new feedback-control methodology

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Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on  (Volume:46 ,  Issue: 5 )