The role of optimal perturbations in improvement of stabil- ity and forecasting capacity of adaptive filter for high di- mensional systems

Abstract

This paper is devoted to an optimal perturbation (OP) which allows to qualify a capacity of the dynamical system to predict more or less correctly the system behaviour in the future. The different types of OPs, deterministic, stochastic, OP in an invariant subspace, are introduced. The theoretical results on the optimality of the introduced OPs are presented. The different simple and efficient numerical algorithms for computation of the OPs are outlined which constitute a basis for implementation of a stable adaptive filter in a very high dimensional environment.