Detail projektu

Identifikace dynamických systémů na časových škálách

Období řešení: 01.01.2016 — 31.12.2018

O projektu

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.

Popis anglicky
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.

Klíčová slova
dynamické systémy; identifikace

Klíčová slova anglicky
dynamical system, identification

Označení

GA16-08549S

Originální jazyk

čeština

Řešitelé

Útvary

Kybernetika pro materiálové vědy
- příjemce (01.01.2016 - nezadáno)

Zdroje financování

Grantová agentura České republiky - Standardní projekty

- plně financující (2016-01-01 - 2018-12-31)

Výsledky

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