An Iterative Procedure for the Identification of Nonlinear Feedback of Noise-Driven Limit-Cycling Systems

We present an iterative procedure, based on results originally established by Mehta and Banaszuk (CDC, 2001), for estimating nonlinear feedback in the context of a noise-driven limit-cycling system, where the pertinent signals contain both Gaussian and harmonic components. The iterative procedure is based on the analysis of random-input describing functions, treated as bounded linear operators on a certain function space. Iterative algorithms are derived for the case when the input signals have a constant variance with varying harmonic amplitudes. This case is relevant when control (or external damping) is applied to a noise-driven limit-cycling system in order to reduce the limit-cycle amplitude. An example is illustrated by numerical simulations.