Random Invariant Measure of Delayed-Feedback Control Systems

Abstract

Delayed-feedback control is applied to stabilize the noise-induced chaotic behavior of a Duffing oscillator and a parametrically excited pendulum with noisy harmonic excitations. We first follow the standard pullback procedure of obtaining random invariant measure (RIM) and then intuitively construct Poincaré maps of RIM. Nonchaotic and chaotic sample processes are stabilized similarly to deterministic delayed-feedback control. The fractal structures of chaotic random processes are stabilized into point structures.