Applied Quadratic Programming with Principles of Statistical Paired Tests

Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 1047)


In applied research areas, various types of mathematical disciplines have been advantageously connected together with wide corresponding applications. As an applied proposal of this connection, a numerical optimization method of the quadratic programming particularly modified by a principle of statistical hypothesis testing can be seen in this paper. With regards to a computational complexity, algorithms of multivariable Model Predictive Control (MPC) can be considered as procedures with a higher computational complexity caused by the multi-variability, higher horizons and included constraints conditions. A wide spectrum of modifications has been proposed in the optimization subsystem of MPC controller yet; however, approaches based on including the hypotheses testing have not been widely considered in applied optimization method. A number of operations should be decreased; however, a control quality may be slightly influenced with regards to this aim. Therefore, the proposed modification is advantageous in an applied form of the quadratic programming technique where necessary information for following steps of a process control are provided. Achieved results are discussed in order to the incorporating of the principle of hypotheses testing in the modified numerical method of the applied quadratic programming.


Hypothesis testing Optimization Quadratic programming Multivariable MPC Control quality 


  1. 1.
    Corriou, J.P.: Process Control: Theory and Applications. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  2. 2.
    Xu, S., Ni, D., Lu, S., et al.: A novel digital multi-mode control strategy with PSM for primary-side flyback converter. Int. J. Electron. 104(5), 840–854 (2017). ISSN 0020-7217CrossRefGoogle Scholar
  3. 3.
    Li, C., Mao, Y., Yang, J., et al.: A nonlinear generalized predictive control for pumped storage unit. Renew. Energy 114, 945–959 (2017). ISSN 0960-1481CrossRefGoogle Scholar
  4. 4.
    Sun, D., Xu, S., Sun, W., et al.: A new digital predictive control strategy for boost PFC converter. IEICE Electron. Exp. 12(23), 9 (2015). ISSN 1349-2543CrossRefGoogle Scholar
  5. 5.
    Zheng, Y., Zhou, J., Zhu, W., et al.: Design of a multi-mode intelligent model predictive control strategy for hydroelectric generating unit. Neurocomputing 207, 287–299 (2016). ISSN 0925-2312CrossRefGoogle Scholar
  6. 6.
    Abraham, A., Pappa, N., Honc, D., et al.: Reduced order modelling and predictive control of multivariable nonlinear process. Sadhana – Acad. Proc. Eng. Sci. 43(3) (2018). ISSN 0256-2499
  7. 7.
    Navratil, P., Pekar, L., Klapka, J.: Load distribution of heat source in production of heat and electricity. Int. Energy J. 17(3), 99–111 (2017). ISSN 1513-718XGoogle Scholar
  8. 8.
    Camacho, E.F., Bordons, C.: Model Predictive Control. Springer, Heidelberg (2004)zbMATHGoogle Scholar
  9. 9.
    Rossiter, J.A.: Model Based Predictive Control: A Practical Approach. CRC Press, Boca Raton (2003)Google Scholar
  10. 10.
    Kwon, W.H.: Receding Horizon Control: Model Predictive Control for State Models. Springer, Heidelberg (2005)Google Scholar
  11. 11.
    Kubalcik, M., Bobal, V., Barot, T.: Modified Hildreth’s method applied in multivariable model predictive control. In: Innovation, Engineering and Entrepreneurship. Lecture Notes in Electrical Engineering, vol. 505, pp. 75–81. Springer (2019). ISBN 978-3-319-91333-9Google Scholar
  12. 12.
    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 (PC), pp. 42–47. IEEE (2015).
  13. 13.
    Wang, L.: Model Predictive Control System Design and Implementation Using MATLAB. Springer, Heidelberg (2009)Google Scholar
  14. 14.
    Dostal, Z.: Optimal Quadratic Programming Algorithms: With Applications to Variational Inequalities. Springer, Heidelberg (2009)zbMATHGoogle Scholar
  15. 15.
    Kitchenham, B., Madeyski, L., Budgen, D., et al.: Robust statistical methods for empirical software engineering. Empir. Softw. Eng. 22, 1–52 (2016)Google Scholar
  16. 16.
    Sulovska, K., Belaskova, S., Adamek, M.: Gait patterns for crime fighting: statistical evaluation. In: Proceedings of SPIE - The International Society for Optical Engineering, vol. 8901. SPIE (2013). ISBN 978-081949770-3
  17. 17.
    Pivarc, J.: Ideas of Czech primary school pupils about intellectual disability. Educ. Stud. Taylor & Francis (2018, in press). ISSN 0305-5698
  18. 18.
    Navratil, P., Balate, J.: One of possible approaches to control of multivariable control loop. IFAC Proc. 40(5), 207–212 (2007). ISSN 1474-6670CrossRefGoogle Scholar
  19. 19.
    Alizadeh Noughabi, H.: Two powerful tests for normality. Ann. Data Sci. 3(2), 225–234 (2016). ISSN 2198-5812CrossRefGoogle Scholar
  20. 20.
    Vaclavik, M., Sikorova, Z., Barot, T.: Particular analysis of normality of data in applied quantitative research. In: Computational and Statistical Methods in Intelligent Systems. Advances in Intelligent Systems and Computing, vol. 859, pp. 353–365. Springer (2019). ISBN 978-3-319-91333-9Google Scholar
  21. 21.
    Hunger, R.: Floating point operations in matrix-vector calculus. (Version 1.3), Technical Report. Technische Universität München, Associate Institute for Signal Processing (2007)Google Scholar
  22. 22.
    Kubalcik, M., Bobal, V.: Adaptive control of coupled drives apparatus based on polynomial theory. Proc. IMechE Part I: J. Syst. Control Eng. 220(I7), 641–654 (2006). Scholar

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Authors and Affiliations

  1. 1.Department of Mathematics with Didactics, Faculty of EducationUniversity of OstravaOstravaCzech Republic
  2. 2.Department of Process Control, Faculty of Applied InformaticsTomas Bata University in ZlinZlinCzech Republic

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