Suppressing Chaos in Uncertain Nonautonomous Oscillators

This paper investigates the control and suppression of chaos in nonautonomous oscillators with uncertain and/or unknown parameters. A nonlinear second order Duffing oscillator that has a single harmonic excitation and two uncertain parameters is used to exemplify the suggested techniques. Only one signal is assumed available for processing, which corresponds to the output of the Duffing oscillator. It is demonstrated that time-delay auto-synchronization, which is a nonmodel-based technique, can force the system to follow a trajectory with period two or three, depending on the parameters of the system, however, it fails to stabilize the system into exhibiting a single period. In contrast, an estimation-based technique that relies on a model-based approach is shown to be superior in forcing the system to follow any prescribed trajectory, including steady set points. Transient performance, stability issues, and tuning optimization are discussed, supported by results, generated from simulations carried out in MATLAB/Simulink environment. In addition, control effort is analyzed and suggestions for compatibility with real-time applications in both science and engineering are presented.