Robust Control of Duffing Oscillators with Unknown Parameters

A new approach to designing a novel controller of the Duffing oscillator is proposed. The problem of tracking control is considered. The control aim is defined as a nonlinear, time-varying ‘funnel’ which must contain the tracking error. The control is based on investigation of tracking error extension which includes information on both state variables. A new, bounded control is derived, reacting when the trajectory approaches the curves constraining the ‘funnel’. The presented approach can be used for chaos synchronization, suppression or for ‘chaotification’ of Duffing oscillators as well as other chaotic systems. The proposed approach is based on a simple robust control concept and does not require complicated stability investigation typical for nonlinear adaptive control.