Control theory approach to shadowing and possible applications

We propose a new approach to so-called shadowing problem i.e. finding a system trajectory which reproduces with a given accuracy the measured time series. Our approach is based on the nonlinear observability problem known in control engineering. Solution of the shadowing problem opens new possibilities for nonlinear signal processing e.g., section-wise approximation of the measured signal by pieces of trajectories from a chosen nonlinear dynamical system (model); signal restoration when the measured signal has been corrupted e.g., by quantization; signal coding and compression.