Adaptive Control of a Nonlinear Oscillating System

A slowly adapting feedforward controller is applied to a nonlinear (Duffing) oscillator. Simulation results show that the adaptation continues relentlessly to improve performance despite the complex system behavior, i.e., the system state passes in and out of both chaotic and multi-periodic attractors, finally settling down to a "quiet" periodic orbit. An analysis is presented based on the method of averaging. Under slow parameter adjustment it is shown that the source of the complex behavior is the nonlineariy in the system being controlled, not that introduced by the adaptation.