Identification of time-varying non-linear systems with adaptive bootstrap-based tracking

The primary intention of the work is to develop a simple and universal method for identifying time-varying nonlinear dynamic systems. No prior knowledge of the structure (Hammerstein or Wiener) and parametric form of static nonlinear characteristics is required. We limit ourselves to the class of so-called ’fading memory systems’, i.e., those that can be approximated with arbitrary accuracy using finite memory models. The proposed identification algorithm is non-parametric in nature and is based on the κ nearest neighbor technique. The distance metric considered is dependent on both the values of the excitations and their timeliness. The original idea is to use an auto-tuning method for the κ parameter based on Efron’s bootstrap technique. This has been proven to guarantee optimal balance between variance and estimator bias. • The time-varying nonlinear dynamic system is identified non-parametrically. • MSE tracking error is minimized automatically using the bootstrap method. • The best bias–variance trade-off is guaranteed asymptotically. • The class of objects considered includes the Hammerstein and Wiener systems. • Cyclostationary input avoids the problem of the curse of multidimensionality.