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

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.