Simultaneous Time-Frequency Synchronization of Non-Autonomous Chaotic Systems

A novel chaos control concept is presented for the synchronization of a non-autonomous chaotic circuit system in the time and frequency domains concurrently. The controller effectively eliminates the differences between two chaotic circuits in the time domain and at the same time restores the characteristics of the driving response in the frequency domain. The simultaneous time-frequency control is achieved through manipulating wavelet coefficients, thus not limited by the increasing bandwidth of the chaotic system — a fundamental restraint that deprives contemporary controller designs of validity and effectiveness. The feedforward feature of the control concept prevents errors from re-entering the control loop and inadvertently perturbing the sensitive chaotic system. Because neither closed-form nor linearization is required, the innate, genuine features of the chaotic response are faithfully retained. The on-line identification feature allows the response system to start at arbitrary initial conditions and to be driven by the sinusoidal forcing term of different amplitudes and phases requiring no knowledge of the system parameters.