bsuirДоклады БГУИРDoklady BGUIR1729-76482708-0382БГУИР10.35596/1729-7648-2022-20-5-21-30bsuir-3409Research ArticleЭЛЕКТРОНИКА, РАДИОФИЗИКА, РАДИОТЕХНИКА, ИНФОРМАТИКАELECTRONICS, RADIOPHYSICS, RADIOENGINEERING, INFORMATICSDual Control of the Extremal Multidimensional Regression ObjectDual Control of the Extremal Multidimensional Regression ObjectМухаВ. С.MukhaV. S.

Муха Владимир Степанович – доктор технических наук, профессор, профессор кафедры информационных технологий автоматизированных систем.

220013, г. Минск, ул. П. Бровки, 6,тел. +375-44 781-16-51

Mukha Vladimir S. – Dr. of Sci., Professor, Professor at the Department of Information Technologies of Automated Systems 

220013, Republic of Belarus, Minsk, P. Brovka St., 6,tel. +375 44 781-16-51

mukha@bsuir.byКакоН. Ф.KakoN. F.

Како Нэнси Фарат – аспирант

220013, г. Минск, ул. П. Бровки, 6

Kako Nancy F. – Postgraduate

220013, Republic of Belarus, Minsk, P. Brovka St., 6

Белорусский государственный университет информатики и радиоэлектроникиBelarusian State University of Informatics and Radioelectronics2022300820222052130Copyright © Муха В.С., Како Н.Ф., 20222022Муха В.С., Како Н.Ф.Mukha V.S., Kako N.F.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://doklady.bsuir.by/jour/article/view/3409

.

The statement of the problem of the dual control of the regression object with multidimensional-matrix input and output variables and dynamic programming functional equations for its solution are given. The problem of the dual control of the extremal regression object, i.e. object response function of which has an extremum, is considered. The purpose of control is reaching the extremum of the output variable by sequential control actions in production operation mode. In order to solve the problem, the regression function of the object is supposed to be quadratic in input variables, and the inner noise is supposed to be Gaussian. The sequential solution of the functional dynamic programming equations is performed. As a result, the optimal control action at the last control step is obtained. It is shoved also that the optimal control actions obtaining at the other control steps is connected with big difficulties and impossible both analytically and numerically. The control action obtained at the last control step is proposed to be used at the arbitrary control step. This control action is called the control action with passive information accumulation. The dual control algorithm with passive information accumulation was programmed for numerical calculations and tested for a number of objects. It showed acceptable results for the practice.

dual controlmultidimensional-matrix regression objectdynamic programmingpassive information accumulationextremal control systemsReferencesMukha V.S., Kako N.F. Dual Control of Multidimensional-matrix Stochastic Objects. Information Technologies and Systems 2019 (ITS 2019): Proceeding of the International Conference, BSUIR, Minsk, 30th October 2019. Minsk: BSUIR; 2019: 236-237.Mukha V.S., Kako N.F. Dual Control of Multidimensional-matrix Stochastic Objects. Information Technologies and Systems 2019 (ITS 2019): Proceeding of the International Conference, BSUIR, Minsk, 30th October 2019. Minsk: BSUIR; 2019: 236-237.Feldbaum A.A. Fundamentals of the theory of the optimal automatic systems. Moscow: Nauka; 1963. (In Russ.)Feldbaum A.A. Fundamentals of the theory of the optimal automatic systems. Moscow: Nauka; 1963. (In Russ.)Feldbaum A.A. Optimal Control Systems. Mathematics in Science and Engineering. A series of monographs and textbooks. Vol. 22. Academic Press, New York and London; 1965.Feldbaum A.A. Optimal Control Systems. Mathematics in Science and Engineering. A series of monographs and textbooks. Vol. 22. Academic Press, New York and London; 1965.Mukha V.S. On the dual control of the inertialess objects. Proceedings of the LETI. 1973;130:31-37. (In Russ.)Mukha V.S. On the dual control of the inertialess objects. Proceedings of the LETI. 1973;130:31-37. (In Russ.)Mukha V.S., Sergeev E.V. Dual control of the regression objects. Proceedings of the LETI. 1976;202:58-64. (In Russ.)Mukha V.S., Sergeev E.V. Dual control of the regression objects. Proceedings of the LETI. 1976;202:58-64. (In Russ.)Mukha V.S. Analysis of multidimensional data. Minsk: Technoprint; 2004. (In Russ.)Mukha V.S. Analysis of multidimensional data. Minsk: Technoprint; 2004. (In Russ.)Mukha V. S., Kako N. F. Total probability and Bayes formulae for joint multidimensional-matrix Gaussian distributions. Vestsі Natsyianal'nai akademіі navuk Belarusі. Seryia fіzіka-matematychnykh navuk = Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics series. 2022;58(1):48-59. DOI: 10.29235/1561-2430-2022-58-1-48-59.Mukha V. S., Kako N. F. Total probability and Bayes formulae for joint multidimensional-matrix Gaussian distributions. Vestsі Natsyianal'nai akademіі navuk Belarusі. Seryia fіzіka-matematychnykh navuk = Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics series. 2022;58(1):48-59. DOI: 10.29235/1561-2430-2022-58-1-48-59.Mukha V.S., Kako N.F. Flat Problem of Allowance Distribution as Dual Control Problem. Information Technologies and Systems 2020 (ITS 2020): Proceeding of the International Conference. BSUIR, Minsk, Belarus, 18th November 2020. Minsk: BSUIR; 2020: 195-196.Mukha V.S., Kako N.F. Flat Problem of Allowance Distribution as Dual Control Problem. Information Technologies and Systems 2020 (ITS 2020): Proceeding of the International Conference. BSUIR, Minsk, Belarus, 18th November 2020. Minsk: BSUIR; 2020: 195-196.

The authors declare that there are no conflicts of interest present.