Project detail

Dynamical Systems Identification on Time-Scales

Duration: 01.01.2016 — 31.12.2018

Funding resources

Czech Science Foundation - Standardní projekty

- whole funder (2016-01-01 - 2018-12-31)

On the project

Projekt je zaměřen na řešení problémů identifikace dynamických systémů na časových škálách. Pro analýzu identifikovatelnosti systémů bude v prvotní fázi řešena otázka stability a pozorovatelnosti. Široké spektrum identifikačních úloh (řešení systémů se zpožděním, stiff systémů s lomeným řádem, rozšíření Bayesovského přístupu k identifikaci o omezení ve formě časově proměnných rovností a nerovností a o nový přístup k fúzi modelů, identifikace systémů použitím ortogonálních funkcí založených na na zobecněných Laguerreových funkcích s lomeným řádem) bude podrobně řešeno moderními metodami. Výstupem projektu bude ucelený přístup k identifikaci časově spojitých a diskrétních modelů na základědiskrétně měřených vstupně/výstupních dat. Důraz bude kladen na analýzu a identifikaci nelineárních a časově proměnných systémů.

Description in English
The project is devoted to solution of problems of identification of dynamical systems on time scales. The stability and observability problem will be solved first as tools for identifiability analysis. A broad spectrum of identification tasks (solving delayed and fractional stiff systems, extension of Bayesian framework for identification by assuming time-variable equality/ inequality constraints and by novel concept of model fusion, identification of systems with orthogonal functions based on generalized Laguerre functions leading to fractional order models) will be rigorously solved by modern methods. The project will provide unified approach to identification of continuous and discrete time models from discrete time input/output measurements. It will place emphasis on analysis and identification of nonlinear and time varying systems.

Keywords
dynamické systémy; identifikace

Key words in English
dynamical system, identification

Mark

GA16-08549S

Default language

Czech

People responsible

Dokoupil Jakub, Ing., Ph.D. - fellow researcher
Jura Pavel, prof. Ing., CSc. - fellow researcher
Matoušek Radomil, prof. Ing., Ph.D. - fellow researcher
Pospíšil Michal, RNDr., Ph.D. - fellow researcher
Rebenda Josef, Mgr., Ph.D. - fellow researcher
Šmarda Zdeněk, doc. RNDr., CSc. - fellow researcher
Tůma Martin, Mgr., Ph.D. - fellow researcher
Vítovec Jiří, Mgr., Ph.D. - fellow researcher
Diblík Josef, prof. RNDr., DrSc. - principal person responsible

Units

Cybernetics in Material Science
- beneficiary (2016-01-01 - not assigned)

Results

ABBADI, A.; MATOUŠEK, R. Hybrid rule-based motion planner for mobile robot in cluttered workspace, A combination of RRT and cell decomposition approaches. Soft Computing, 2016, vol. 2016, no. 1, p. 1-17. ISSN: 1433-7479.
Detail

LANG, S.; MATOUŠEK, R.; ŠVARC, I. Two-Degree-of-Freedom Controller Tuning. Mendel Journal series, 2018, vol. 24, no. 2, p. 37-40. ISSN: 1803-3814.
Detail

POSPÍŠIL, M. Representation of solutions of delayed difference equations with linear parts given by pairwise permutable matrices via Z-transform. APPLIED MATHEMATICS AND COMPUTATION, 2017, vol. 294, no. 3, p. 180-194. ISSN: 0096-3003.
Detail

RYBA, L.; DOKOUPIL, J.; VODA, A.; BESANCON, G. Adaptive hysteresis compensation on an experimental nanopositioning platform. INTERNATIONAL JOURNAL OF CONTROL, 2016, vol. 1, no. 1, p. 1-14. ISSN: 1366-5820.
Detail

DOKOUPIL, J.; VÁCLAVEK, P. Design of variable exponential forgetting for estimation of the statistics of the Normal distribution. In 55th Conference on Decision and Control. IEEE, 2016. p. 1179-1184. ISBN: 978-1-5090-1837-6.
Detail

STEVIČ, S.; IRIČANIN, B.; ŠMARDA, Z. Solvability of a close to symmetric system of difference equations. Electronic Journal of Differential Equations, 2016, vol. 2016, no. 159, p. 1-13. ISSN: 1072-6691.
Detail

TŮMA, M.; JURA, P. Continuous Time Models Identification with Laguerre Functions. In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2016). AIP conference proceedings. Rhodos: American Institute of Physics, 2017. p. 480011-1 (480011-4 p.)ISBN: 978-0-7354-1538-6. ISSN: 0094-243X.
Detail

DIBLÍK, J. Exponential stability of linear discrete systems with nonconstant matrices and nonconstant delay. In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2016). AIP conference proceedings. Rhodos: American Institute of Physics, 2017. p. 480003-1 (480003-4 p.)ISBN: 978-0-7354-1538-6. ISSN: 0094-243X.
Detail

POSPÍŠIL, M. Relative controllability of delayed difference equations to multiple consecutive states. In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2016). AIP conference proceedings. Rhodos: American Institute of Physics, 2017. p. 480002-1 (480002-4 p.)ISBN: 978-0-7354-1538-6. ISSN: 0094-243X.
Detail

REBENDA, J.; ŠMARDA, Z.; KHAN, Y. A New Semi-analytical Approach for Numerical Solving of Cauchy Problem for Differential Equations with Delay. FILOMAT, 2017, vol. 31, no. 15, p. 4725-4733. ISSN: 0354-5180.
Detail

DIBLÍK, J. Exponential stability of linear discrete systems with variable delays via Lyapunov Second method. DISCRETE DYNAMICS IN NATURE AND SOCIETY, 2017, vol. 2017, no. 1, p. 1-9. ISSN: 1026-0226.
Detail

MARADA, T.; MATOUŠEK, R.; ZUTH, D. DESIGN OF LINEAR QUADRATIC REGULATOR (LQR) BASED ON GENETIC ALGORITHM FOR INVERTED PENDULUM. Mendel Journal series, 2017, vol. 23 (2017), no. 1, p. 149-156. ISSN: 1803-3814.
Detail

BAŠTINEC, J.; DIBLÍK, J.; SHATYRKO, A.; KHUSAINOV, D. Исследование динамики одной слабонелинейной системы с запаздыванием. Проблемы управления и нфоматики, 2018, roč. 2018, č. 1, s. 22-37. ISSN: 0572-2691.
Detail

DIBLÍK, J.; DEMCHENKO, H.; BAŠTINEC, J.; KHUSAINOV, D. Exponential Stability of Linear Discrete Systems with Multiple Delays. Discrete Dynamics in Nature and Society, 2018, vol. 2018, no. 2018, p. 1-7. ISSN: 1607-887X.
Detail

REBENDA, J.; ŠMARDA, Z. Numerical Solution of Fractional Control Problems via Fractional Differential Transformation. In Proceedings of European Conference on Electrical Engineering and Computer Science 2017. 2017. p. 107-111. ISBN: 978-1-5386-2085-4.
Detail

TŮMA, M.; JURA, P. Optimal parameters for the generalized Laguerre identification method. In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2017). AIP conference proceedings. American Institute of Physics, 2018. p. 430012-1 (430012-4 p.)ISBN: 978-0-7354-1690-1. ISSN: 0094-243X.
Detail

TŮMA, M.; JURA, P. Dead time approximation of LTI SISO systems in time domain using generalized Laguerre functions. In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2017). AIP conference proceedings. American Institute of Physics, 2018. p. 430013-1 (430013-4 p.)ISBN: 978-0-7354-1690-1. ISSN: 0094-243X.
Detail

TŮMA, M.; JURA, P. Comparison of different approaches to continuous-time system identification from sampled data. In 2017 European Conference on Electrical Engineering and Computer Science (EECS) (2017). 2017. p. 61-65. ISBN: 978-1-5386-2085-4.
Detail

DIBLÍK, J.; SVOBODA, Z. Asymptotic properties of delayed matrix exponential function via Lambert function. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2018, vol. 72, no. 10, p. 123-144. ISSN: 1553-524X.
Detail

DIBLÍK, J.; KHUSAINOV, D.; RŮŽIČKOVÁ, M. Exponential Stability of Linear Discrete Systems with Delay. In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2017). AIP conference proceedings. AMER INST PHYSICS, 2 HUNTINGTON QUADRANGLE, STE 1NO1, MELVILLE, NY 11747-4501 USA: American Institute of Physics, 2018. p. 430004-1 (430004-4 p.)ISBN: 978-0-7354-1690-1. ISSN: 0094-243X.
Detail

BAŠTINEC, J.; DIBLÍK, J.; KHUSAINOV, D. Stability of Linear Discrete Systems with Variable Delays. In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2017). AIP conference proceedings. AMER INST PHYSICS, 2 HUNTINGTON QUADRANGLE, STE 1NO1, MELVILLE, NY 11747-4501 USA: American Institute of Physics, 2018. p. 430005-1 (430005-4 p.)ISBN: 978-0-7354-1690-1. ISSN: 0094-243X.
Detail

DOKOUPIL, J.; VÁCLAVEK, P. Adaptive fading Kalman filter design using the geometric mean of normal probability densities. In 2018 Annual American Control Conference. IEEE, 2018. p. 5037-5042. ISBN: 978-1-5386-5428-6.
Detail

DOKOUPIL, J.; VÁCLAVEK, P. Data-driven stabilized forgetting design using the geometric mean of normal probability densities. In 57th Conference on Decision and Control. IEEE, 2018. p. 1403-1408. ISBN: 978-1-5386-1394-8.
Detail

KHUSAINOV, D.; DIBLÍK, J.; BAŠTINEC, J.; SHATYRKO, A. Investigating dynamics of one weakly nonlinear system with delay argument. Journal of automation and information sciences, 2018, vol. 50, no. 1, p. 20-38. ISSN: 1064-2315.
Detail

ŠMARDA, Z. Numerical Solving Linear Systems of Stiff Delay Differential Equations with Constant Delays. Advances in Intelligent Systems and Computing, 2019, vol. 2019, no. 837, p. 299-310. ISSN: 2194-5357.
Detail

REBENDA, J.; ŠMARDA, Z. Solutions to delayed fractional differential equations of second order. In International Conference of Numerical Analysis and Applied Mathematics, ICNAAM 2018. AIP conference proceedings. 2019. p. 1-4. ISBN: 9780735418547. ISSN: 0094-243X.
Detail

BAŠTINEC, J.; DIBLÍK, J.; MENCÁKOVÁ, K. Initial data generating bounded solutions of .systems of linear discrete equations. In AIP Conference Proceedings 2116, 310011 (2019). AIP conference proceedings. AIP, 2019. p. 310011-1 (310011-4 p.)ISBN: 9780735418547. ISSN: 0094-243X.
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DIBLÍK, J.; RŮŽIČKOVÁ, M.; VÁŽANOVÁ, G. Exponential-type estimates of solutions linear discrete systems with constant coefficients and single delay. In AIP Conference Proceedings 2116. AIP conference proceedings. AIP, 2019. p. 310002-1 (310002-4 p.)ISBN: 9780735418547. ISSN: 0094-243X.
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DIBLÍK, J.; SVOBODA, Z. Existence of strictly decreasing positive solutions of linear differential equations of neutral type. In AIP Conference Proceedings 2116. AIP conference proceedings. AIP, 2019. p. 310005-1 (310005-4 p.)ISBN: 9780735418547. ISSN: 0094-243X.
Detail

TŮMA, M.; JURA, P. Choice of time-scale parameter for dead time estimation in Laguerre basis. In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2018). AIP conference proceedings. 2019. p. 310009-1 (310009-4 p.)ISBN: 978-0-7354-1854-7. ISSN: 0094-243X.
Detail

TŮMA, M.; JURA, P. Impulse response approximation of dead time LTI SISO systems using generalized Laguerre functions. In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2018). AIP conference proceedings. 2019. p. 310010-1 (310010-4 p.)ISBN: 978-0-7354-1854-7. ISSN: 0094-243X.
Detail

DIBLÍK, J. Relative and Trajectory Controllability of Linear Discrete Systems With Constant Coefficients and a Single Delay. IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2019, vol. 64, no. 5, p. 2158-2165. ISSN: 0018-9286.
Detail

BEREZANSKY, L.; DIBLÍK, J.; SVOBODA, Z.; ŠMARDA, Z. Exponential Stability Tests for Linear Delayed Differential Systems Deepending on All Delayes. Journal of Dynamics and Differential Equations, 2019, vol. 2019, no. 31, p. 2095-2108. ISSN: 1572-9222.
Detail

DIBLÍK, J.; SVOBODA, Z. Existence of Strictly Decreasing Positive Solutions of Linear Differential Equations of Neutral Type. Discrete and Continuous Dynamical Systems - Series S, 2020, vol. 13, no. 1, p. 67-84. ISSN: 1937-1632.
Detail

JURA, P.; TŮMA, M.: FM2016; modulová stavebnice pro realizaci fyzikálních modelů diferenciálních rovnic. Ústav UAMT, Technická 3082/12, 61600 Brno. (funkční vzorek)
Detail

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