Detail projektu

Identifikace nelineárních dynamických systémů zlomkového řádu

Období řešení: 01.01.2019 — 31.12.2021

Zdroje financování

Grantová agentura České republiky - Standardní projekty

- plně financující (2019-02-22 - 2021-12-31)

O projektu

Projekt je zaměřen na řešení problému identifikace nelineárních dynamických systémů s využitím modelů se zlomkovými derivacemi. S tím souvisí výzkum metod analýzy systémů se zlomkovým řádem - zlomkových systémů (úlohy o stabilitě zlomkových systémů se zpožděním, úlohy řiditelnosti a pozorovatelnosti pro zlomkové systémy se zpožděním a jejich numerická řešení) a následný vývoj originálních metod pro adaptivní odhad zlomkových systémů pomocí Bayesovského přístupu a identifikace zlomkových systémů Laguerrovou identifikací. Výstupem projektu budou nové přístupy k identifikaci dynamických systémů založených na zlomkových modelech. Důraz bude kladen na analýzu a identifikaci nelineárních a časově proměnných systémů.

Popis anglicky
The project focuses on solving the problem of identification of nonlinear fractional dynamical systems using models with fractional derivatives. With this is related investigation of methods of analysis of systems with fractional order – fractional systems (fractional delay stability problems, control and observability problems for fractional delayed systems and their numerical solution) and subsequent research of original methods for adaptive estimation of fractional systems from the Bayesian perspective and Laguerre based identification of fractional order systems. As outputs the project will provide new approaches to the identification of dynamical systems based on fractional models. An emphasis will be placed on the analysis and identification of nonlinear and time varying systems.

Klíčová slova
identifikace; nelinearita; zlomková derivace; dynamický systém;

Klíčová slova anglicky
identification; nonlinearity; fractional derivative; dynamical system;

Označení

19-23815S

Originální jazyk

čeština

Řešitelé

Diblík Josef, prof. RNDr., DrSc. - hlavní řešitel
Baštinec Jaromír, RNDr., CSc. - spoluřešitel
Dokoupil Jakub, Ing., Ph.D. - spoluřešitel
Jura Pavel, prof. Ing., CSc. - spoluřešitel
Kárský Vilém, Ing. - spoluřešitel
Rebenda Josef, Mgr., Ph.D. - spoluřešitel
Šmarda Zdeněk, doc. RNDr., CSc. - spoluřešitel
Tůma Martin, Mgr., Ph.D. - spoluřešitel

Útvary

Kybernetika pro materiálové vědy
- příjemce (01.01.2019 - 31.12.2021)

Výsledky

REBENDA, J. Application of Differential Transform to Multi-Term Fractional Differential Equations with Non-Commensurate Orders. Symmetry, 2019, vol. 11, no. 11, p. 1-10. ISSN: 2073-8994.
Detail

TŮMA, M.; JURA, P.; KÁRSKÝ, V. Approximation of r-th Order Dead Time System Using Generalized Laguerre Functions. In AIP Conference Proceedings. AIP conference proceedings. MELVILLE: AMER INST PHYSICS, 2024. p. 1-4. ISBN: 978-07-3544-954-1. ISSN: 0094-243X.
Detail

DOKOUPIL, J.; VÁCLAVEK, P. Variable exponential forgetting for estimation of the statistics of the normal-Wishart distribution with a constant precision. In 58th Conference on Decision and Control. Nice, France: IEEE, 2019. p. 5094-5100. ISBN: 978-1-7281-1397-5.
Detail

KÁRSKÝ, V. An Improved Method for Parameterizing Generalized Laguerre Functions to Compute the Inverse Laplace Transform of Fractional Order Transfer Functions. In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2019. 2020. p. 340004-1 (340004-4 p.)ISBN: 978-0-7354-4025-8.
Detail

KÁRSKÝ, V.; TŮMA, M.; JURA, P. Approximation of the Fractional Order Transfer Functions with Integer Order Transfer Functions. In International Conference on Numerical Analysis and Applied Mathematics 2020, ICNAAM 2020. AIP conference proceedings. 2425. American Institute of Physics Inc., 2022. p. 270004-1 (270004-5 p.)ISBN: 9780735441828. ISSN: 0094-243X.
Detail

DIBLÍK, J.; BAŠTINEC, J. Existence of solutions of discrete equations of Volterra type in prescribed domains and fractional discrete equations. In Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2019 (ICNAAM-2019). AIP conference proceedings. Melville (USA): AIP, 2020. p. 340007-1 (340007-4 p.)ISBN: 978-0-7354-4025-8. ISSN: 0094-243X.
Detail

BAŠTINEC, J.; DIBLÍK, J.; PINELAS, S. Initial data generating bounded solutions of a system of two linear discrete equations. In Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2019 (ICNAAM-2019). AIP conference proceedings. Melville (USA): AIP, 2020. p. 340010-1 (340010-4 p.)ISBN: 978-0-7354-4025-8. ISSN: 0094-243X.
Detail

TŮMA, M.; JURA, P. Dead Time Estimation in Generalized Laguerre Functions Basis. In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2019. AIP conference proceedings. 2020. p. 340005-1 (340005-4 p.)ISBN: 978-0-7354-4025-8. ISSN: 0094-243X.
Detail

TŮMA, M.; JURA, P. Approximation of First Order Dead Time System Using Generalized Laguerre Functions. In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2019. AIP conference proceedings. 2020. p. 340006-1 (340006-4 p.)ISBN: 978-0-7354-4025-8. ISSN: 0094-243X.
Detail

DOKOUPIL, J.; VÁCLAVEK, P. Regularized estimation with variable exponential forgetting. In 59th Conference on Decision and Control. New York: IEEE, 2020. p. 312-318. ISBN: 978-1-7281-7446-4.
Detail

DOKOUPIL, J.; VÁCLAVEK, P. Recursive identification of the Hammerstein model based on the Variational Bayes method. In 60th IEEE Conference on Decision and Control. NEW YORK: IEEE, 2021. p. 1586-1591. ISBN: 978-1-6654-3659-5.
Detail

DIBLÍK, J.; KHUSAINOV, D.; SHATYRKO, A.; BAŠTINEC, J.; SVOBODA, Z. Absolute Stability of Neutral Systems with Lurie Type Nonlinearity. Advances in Nonlinear Analysis, 2022, vol. 11, no. 1, p. 726-740. ISSN: 2191-950X.
Detail

TŮMA, M.; JURA, P.; KÁRSKÝ, V. Approximation of second order dead time system using generalized Laguerre functions. In International Conference on Numerical Analysis and Applied Mathematics 2020, ICNAAM 2020. AIP conference proceedings. 2425. American Institute of Physics Inc., 2022. p. 270005-1 (270005-4 p.)ISBN: 9780735441828. ISSN: 0094-243X.
Detail

TŮMA, M.; JURA, P.; KÁRSKÝ, V. Comparison of dead time estimations methods for dynamical systems. In International Conference on Numerical Analysis and Applied Mathematics 2020, ICNAAM 2020. AIP conference proceedings. 2425. American Institute of Physics Inc., 2022. p. 270006-1 (270006-4 p.)ISBN: 9780735441828. ISSN: 0094-243X.
Detail

DIBLÍK, J.; BAŠTINEC, J. Bounded solutions of fractional discrete equations of positive non-integer orders. In ICNAAM 2020 PROCEEDINGS - AIP CP Volume 2425. AIP conference proceedings. Melville (USA): 2022. p. 270003-1 (270003-4 p.)ISBN: 978-0-7354-4182-8. ISSN: 0094-243X.
Detail

DIBLÍK, J. Bounded solutions to systems of fractional discrete equations. Advances in Nonlinear Analysis, 2022, vol. 11, no. 1, p. 1614-1630. ISSN: 2191-950X.
Detail

DOKOUPIL, J.; VÁCLAVEK, P. Recursive identification of time-varying Hammerstein systems with matrix forgetting. IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2023, vol. 68, no. 5, p. 3078-3085. ISSN: 0018-9286.
Detail

ŠMARDA, Z. Laplace Adomian Decomposition Method for Solving Fractional Delay Differential Equations with Variable Coefficients. In Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2021 (ICNAAM-2021). AIP conference proceedings. 2023. p. 1-4. ISSN: 0094-243X.
Detail

DIBLÍK, J. Asymptotic behaviour of particular solutions of nonhomogeneous linear fractional discrete equations. In AIP Conference Proceedings, International Conference on Numerical Analysis and Applied Mathematics 2021, ICNAAM 2021. AIP conference proceedings. Melville (USA): American Institute of Physics, 2023. p. 370001-1 (370001-4 p.)ISSN: 0094-243X.
Detail

BAŠTINEC, J.; DIBLÍK, J. Bounded solutions of discrete equations with several fractional differences. In AIP Conference Proceedings, Volume 3094, Issue 1, 7 June 2024, International Conference of Numerical Analysis and Applied Mathematics 2022, ICNAAM 2022. AIP conference proceedings. USA: American Institute of Physics, 2024. p. 500044-1 (500044-4 p.)ISBN: 9780735449541. ISSN: 0094-243X.
Detail

TŮMA, M.; KÁRSKÝ, V.; JURA, P. Comparison of Identification Methods for Dynamical System Models in a Single Chip. In AIP Conference Proceedings. AIP conference proceedings. MELVILLE: AMER INST PHYSICS, 2024. p. 1-4. ISBN: 978-07-3544-954-1. ISSN: 0094-243X.
Detail

DOKOUPIL, J.; VÁCLAVEK, P. Forgetting factor Kalman filter with dependent noise processes. In 58th Conference on Decision and Control. Nice, France: IEEE, 2019. p. 1809-1815. ISBN: 978-1-7281-1397-5.
Detail

Odpovědnost: Diblík Josef, prof. RNDr., DrSc.