Author, institution: Mantas Landauskas, Kaunas University of Technology
Science area, field: Physical sciences, Informatics – 09P
The Doctoral Dissertation is available at the library of Kaunas University of Technology (K. Donelaičio St. 20, Kaunas).
Scientific Supervisor: Prof. Dr. Habil. Minvydas Kazys RAGULSKIS, Kaunas University of Technology
Dissertation defence board of Informatics Science Field:
Prof. Dr. Habil. Rimantas BARAUSKAS (Kaunas University of Technology, physical sciences, informatics – 09P) – chairman;
Prof. Dr. Romas BARONAS (Vilnius University, Physical sciences, informatics – 09P);
Prof. Dr. Habil. Vytautas KAMINSKAS (Vytautas Magnus University, Physical sciences, informatics – 09P);
Prof. Dr. Gintaras PALUBECKIS (Kaunas University of Technology, physical sciences, informatics – 09P;
Prof. Dr. Jonas RIMAS (Kaunas University of Technology, physical sciences, informatics – 09P);
Prof. dr. Miguel A. F. SANJUAN (Rey Juan Carlos University, Spain, physical sciences, informatics – 09).
Hankel matrices are broadly applied to problems such as system identification, the exploration of the onset of chaos in discrete nonlinear dynamical systems, sensitivity to initial conditions in nonlinear systems. The concept of the H-rank was developed in the thesis by analyzing nonlinear dynamical systems, forecasting short time series.
H-ranks (or pseudoranks to be exact) enables to identify the stable manifold, the unstable manifold and the manifold of non-asymptotic convergence in the plane of system’s parameters. These results were later used to develop control techniques for discrete and continuous dynamical systems. Aspects of floating point arithmetic for computations of H-ranks are considered and LAPACK package is employed which significantly reduces the time required to compute parameter planes of H-ranks compared to MATLAB computation time. Concepts of algebraic analysis (rank of a linear recurrence sequence) had been also used in forecasting short time series while considering signals of the real world magnetometer.
The development of the theory of H-ranks is the main value of this work as H-rank based algorithms enable to reveal and/or solve a set of new system identification, forecasting and control problems.