056. Identification of the systems of linear difference equations

Our work is devoted to studying identification problems for linear difference equations and control theory systems. Such identification problems arise in vast variety of applications including geophysics, engineering, economics, bioinformatics etc. There are many popular modern approaches for solving such problems which are based on having relatively large number of observations. However, in real applications the number of observations can be quite small and the number of unknowns can be relatively large. In the present work we consider the problems with such features. Our main results are: algorithms for constructing approximations of the solutions of identification problem having the small number of observations based on modifications of  Prony’s method; the proof of convergence of the iteration process and the estimates of  rate of convergence; the stability estimates of the solutions given the perturbations in the observation data. For this work we have developed the program implementation for solving the considered identification problems optimized for modern high-performance multiprocessor systems.