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Geometrical Modelling Applied on Particular Constrained Optimization Problems

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Software Engineering Perspectives in Intelligent Systems (CoMeSySo 2020)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 1295))

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Abstract

In favour of proposals of modified control techniques, geometrical analyses of the theoretical background of parts of the control algorithms should be advantageous. Concretely, the nonlinear optimization has been frequently considered as one of the important parts of the modern control strategies, e.g. the predictive control. Due to improving the control quality and minimization of control errors, the quadratic cost function can be generally included in the control algorithms. Therefore, the applied type of the nonlinear optimization is frequently specified as the quadratic programming problem with constraints. In this paper, the most occurred situations in this quadratic programming are geometrically modelled according to the stereo-metrical approach using the GeoGebra software. Advantages of achieved results can be suitably applied in the further proposals of the modified control methods.

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References

  1. Corriou, J.P.: Process Control: Theory and Applications. Springer, Heidelberg (2004)

    Book  Google Scholar 

  2. Huang, S.: Applied predictive control. Springer, Heidelberg (2002)

    Google Scholar 

  3. Wang, L.: Model Predictive Control System Design and Implementation Using MATLAB. Springer, Heidelberg (2009)

    Google Scholar 

  4. Dostal, Z.: Optimal Quadratic Programming Algorithms: With Applications to Variational Inequalities. Springer, Heidelberg (2009)

    MATH  Google Scholar 

  5. Ingole, D., Holaza, J., Takacs, B., et al.: FPGA-based explicit model predictive control for closed loop control of intravenous anesthesia. In: 20th International Conference on Process Control, pp. 42−47. Institute of Electrical and Electronics Engineers Inc. (2015). https://doi.org/10.1109/PC.2015.7169936

  6. Belda, K.: On-line solution of system constraints in generalized predictive control design: convenient way to cope with constraints. In: 20th International Conference on Process Control, pp. 25–30. Institute of Electrical and Electronics Engineers Inc. (2015). https://doi.org/10.1109/PC.2015.7169933

  7. Barot, T., Krpec, R., Kubalcik, M.: Applied quadratic programming with principles of statistical paired tests. In: Computational Statistics and Mathematical Modeling Methods in Intelligent Systems, Advances in Intelligent Systems and Computing, vol. 1047, pp. 278−287. Springer, Heidelberg (2019). ISBN 978–3–030–31361–6. https://doi.org/10.1007/978-3-030-31362-3_27

  8. Barot, T., Burgsteiner, H., Kolleritsch, W.: Comparison of discrete autocorrelation functions with regards to statistical significance. In: Advances in Intelligent Systems and Computing. Springer, Heidelberg (2020). ISSN 2194–5357 (in Print)

    Google Scholar 

  9. Burgsteiner, H., Kroll, M., Leopold, A., et al.: Movement prediction from real-world images using a liquid state machine. Appl. Intell. 26(2), 99–109 (2007). https://doi.org/10.1007/s10489-006-0007-1

    Article  Google Scholar 

  10. Barta, C., Kolar, M., Sustek, J.: On Hessians of composite functions. Appl. Math. Sci. 8(172), 8601–8609 (2014). https://doi.org/10.12988/ams.2014.410805

  11. Vaclavik, M., Sikorova, Z., Barot, T.: Approach of process modeling applied in particular pedagogical research. In: Cybernetics and Automation Control Theory Methods in Intelligent Algorithms, Advances in Intelligent Systems and Computing, vol. 986, pp. 97–106. Springer, Heidelberg (2019). https://doi.org/10.1007/978-3-030-19813-8_11

  12. Schmidt, W.M., Summerer, L.: Parametric geometry of numbers and applications. Acta Arithmetica 140(1), 67–91 (2009). https://doi.org/10.4064/aa140-1-5

    Article  MathSciNet  MATH  Google Scholar 

  13. GeoGebra Homepage. https://www.geogebra.org. Accessed 14 May 2020

  14. Vagova, R., Kmetova, M.: The role of visualisation in solid geometry problem solving. In: 17th Conference on Applied Mathematics, pp. 1054–1064. STU Bratislava. (2018)

    Google Scholar 

  15. Duris, V., Sumny, T., Pavlovicova, G.: Student solutions of non-traditional geometry tasks. TEM J. 8(2), 642–647 (2019)

    Google Scholar 

  16. Lavicza, Z., Papp-Varga, Z.: Integrating GeoGebra into IWB-equipped teaching environments: preliminary results. Technol. Pedagogy Educ. 19(2), 245–252 (2010). https://doi.org/10.1080/1475939X.2010.491235

    Article  Google Scholar 

  17. Korenova, L.: GeoGebra in teaching of primary school mathematics. Int. J. Technol. Math. Educ. 24(3), 155–160 (2017)

    Google Scholar 

  18. Arzarello, F., Ferrara, F., Robutti, O.: Mathematical modelling with technology: the role of dynamic representations. Teach. Math. Appl. 31(1), 20–30 (2012). https://doi.org/10.1093/teamat/hrr027

    Article  Google Scholar 

  19. Vallo, D., Duris, V.: Geogebra and logarithmic spiral in educational process. In: 17th Conference on Applied Mathematics, pp. 1076–1082. STU Bratislava (2018)

    Google Scholar 

  20. Navratil, P., Pekar, L., Matusu, R.: Control of a multivariable system using optimal control pairs: a quadruple-tank process. IEEE Access 8, 2537–2563 (2020). https://doi.org/10.1109/ACCESS.2019.2962302

    Article  Google Scholar 

  21. Pekar, L., Gazdos, F.: A potential use of the balanced tuning method for the control of a class of time-delay systems. In: 22th International Conference on Process Control, pp. 161–166. Institute of Electrical and Electronics Engineers Inc. (2019)

    Google Scholar 

  22. Chramcov, B., Marecki, F., Bucki,R.: Heuristic control of the assembly line. Advances in Intelligent Systems and Computing, vol. 348, 189−198. Springer (2015). ISBN 978–3–319–18502–6. https://doi.org/10.1007/978-3-319-18503-3_19

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Acknowledgements

This paper was realized with the financial support of the SGS project at University of Ostrava, Faculty of Education: SGS05/PdF/2019–2020.

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Authors and Affiliations

  1. Department of Mathematics with Didactics, Faculty of Education, University of Ostrava, Fr. Sramka 3, 709 00, Ostrava, Czech Republic

    Lilla Korenova, Tomas Barot & Radek Krpec

  2. Department of Mathematics, Faculty of Science, Constantine the Philosopher University in Nitra, Trieda A. Hlinku 1, 949 74, Nitra, Slovakia

    Renata Vagova

Authors
  1. Lilla Korenova
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  2. Renata Vagova
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  3. Tomas Barot
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  4. Radek Krpec
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Corresponding author

Correspondence to Tomas Barot .

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Editors and Affiliations

  1. Faculty of Applied Informatics, Tomas Bata University in Zlín, Zlín, Czech Republic

    Radek Silhavy

  2. Faculty of Applied Informatics, Tomas Bata University in Zlín, Zlín, Czech Republic

    Petr Silhavy

  3. Faculty of Applied Informatics, Tomas Bata University in Zlín, Zlín, Czech Republic

    Zdenka Prokopova

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Korenova, L., Vagova, R., Barot, T., Krpec, R. (2020). Geometrical Modelling Applied on Particular Constrained Optimization Problems. In: Silhavy, R., Silhavy, P., Prokopova, Z. (eds) Software Engineering Perspectives in Intelligent Systems. CoMeSySo 2020. Advances in Intelligent Systems and Computing, vol 1295. Springer, Cham. https://doi.org/10.1007/978-3-030-63319-6_16

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