Recovering unknown model parameters contained in a class of time-variant chaotic dynamical systems

This work deals mainly with the problem of recovering all unknown parameters for a class of time-variant chaotic dynamical systems from given time sequence. Based on synchronization between a chaotic sender system and an additional receiver system, a procedure, which combines a linear feedback technique with updated feedback gain and an adapted control strategy associated with the law of estimated parameters, is developed to dynamically determine the values of unknown parameters contained in the sender system. To promote widespread applications, the structure of the receiver system can be independent of that of the sender system. The effectiveness of this procedure is guaranteed by the periodic version of the classical LaSalle invariance principle of differential equations. Illustrations are presented for a harmonically excited Duffing oscillator and a four dimensional chaotic oscillator. The numerical results reveal the present procedure not only can precisely recover unknown model parameters, but also can rapidly response to sudden changes in unknown parameters. In addition, it has great robustness against the disturbance of noise.