On solving dynamic programming problems in the Wolfram Mathematica system

V.R. Kristalinskii, S.N. Chernyi

Abstract


The computer mathematics systems can make sufficiently higher the effectiveness of solving of many applied problems, particularly probems, which can be solved using the method of dynamical programming. Such  problems are  considered very often by solving the problems of the optimal governing in economics and military science. In this problems is usually needs to obtain the optimal distribution of the resources between the consumers. Earlier the solution of such problems particularly for the big volumes of data was connected with serious difficulties. The construction of the multistep scheme of the solution connected with the difficulties of two sorts. By the first, it is not simple to choose the parameters of the state of the system. By the second, in many cases it is difficult to divide the solution on the steps. The usage of Wolfram Mathematica system allows to solve such problems as usual problems of the integer programming. As the examples in the work were considered the problem of target distribution, the problem of reliability of the technical system, the problem of the distribution of the resources and some other. This methodic can be used in the scientific researches, by the solving of applied problems, by the teaching in the civil and military educational organizations of the disciplines connected with the operation research and the governing solutions.


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References


Bellman R. Prikladny`e zadachi dinamicheskogo programmirovaniya. – Ripol Klassik, 2013.

Ventcel` E.S. Issledovanie operacij.– M.: Sovetskoe radio, 1972.–357 s.

Ventcel` E. S. E`lementy` dinamicheskogo programmirovaniya.– M.: Nauka, 1964.–176 s.

Sutyagina N. I. Metod dinamicheskogo programmirovaniya pri prinyatii mikroe`kono-micheskogo resheniya //Vestnik NGIE`I. – 2014. – №. 11 (42).

Posy`pkin M. A., Sin S. T. T. O rasparallelivanii metoda dinamicheskogo program-mirovaniya dlya zadachi o rance //International Journal of Open Information Technologies. – 2017. – T. 5. – №. 7.

Guseva A. V., Burkovskij V. L., Gusev K. Yu. Modelirovanie processa prinyatiya reshe-nij na osnove apparata dinamicheskogo programmirovaniya //BBK 3.30 (ya4) Novy`e texnologii v nauch-ny`x issledovaniyax, proektirovanii, upravlenii, proizvodstve: trudy` Mezhdunar. nauch.-texn. konf. Voronezh: FGBOU VO «Voronezhskij gosudarstvenny`j texnicheskij universitet», 2017, T. 1, 404 s. ISBN 978-5-7731-0567-1. – 2017. – S. 252.

Karaseva R. B. Optimal`noe raspredelenie investicij po ob``ektam vlozheniya metoda-mi dinamicheskogo programmirovaniya //Koncept. – 2016. – №. 7.

Raxmangulov A. N., Mishkurov P. N. Problemy` ispol`zovaniya metodov dinamicheskogo programmirovaniya dlya operativnogo upravlenii vagonopotokami //Sovremenny`e problemy` trans-portnogo kompleksa Rossii. – 2018. – T. 2. – №. 1. – S. 279-285.

Elizarov D. E`., Burkovskij V. L. Model` optimal`nogo razvitiya struktury` mul`ti-servisny`x setej na osnove apparata dinamicheskogo programmirovaniya //Vestnik Voronezhskogo gosu-darstvennogo texnicheskogo universiteta. – 2016. – T. 12. – №. 1.

Bajramukov S. X., Dolaeva Z. N., Omarov A. O. O metodax dinamicheskogo programmi-rovaniya processov kompleksnoj modernizacii zhilishhnogo fonda //Vestnik Dagestanskogo gosudarst-vennogo texnicheskogo universiteta. Texnicheskie nauki. – 2015. – T. 38. – №. 3.

Grigor`ev A. M. Reshenie zadachi ob optimal`nom raspredelenii zadanij metodom di-namicheskogo programmirovaniya s primeneniem parallel`ny`x vy`chislenij //Vestnik Udmurtskogo universiteta. Matematika. Mexanika. Komp`yuterny`e nauki. – 2017. – T. 27. – №. 1. – S. 129-137.

Elizarov D. E`., Burkovskij V. L. Modifikaciya metoda Bellmana resheniya dinamiche-skoj zadachi o rance //Vestnik Voronezhskogo gosudarstvennogo texnicheskogo universiteta. – 2015. – T. 11. – №. 5.

Frolov S. V. Formirovanie optimal`noj investicionnoj politiki predpriyatij s pomoshh`yu metoda dinamicheskogo programmirovaniya //MOLODY`E ISSLEDOVATELI OBRAZOVA-NIYa. – 2017. – S. 313.

Pegachkova E. A., Kuzneczova E. L., Gorbunova Yu. A. Upravlenie bespilotny`m samole-tom metodom dinamicheskogo programmirovaniya v teorii grafov //Izvestiya Tul`skogo gosudarstvenno-go universiteta. Texnicheskie nauki. – 2016. – №. 11-2.

Posy`pkin M. A., Si T. T. S. Sravnitel`ny`j analiz e`ffektivnosti razlichny`x varian-tov metoda dinamicheskogo programmirovaniya dlya resheniya optimizacionny`x zadach na e`tape razmeshhe-niya e`lementov mikrosxem //Problemy` razrabotki perspektivny`x mikro-i nanoe`lektronny`x sistem (ME`S). – 2014. – №. 2. – S. 97-100.

Zhang, Huaguang, et al. "Leader-based optimal coordination control for the consensus problem of multiagent differential games via fuzzy adaptive dynamic programming." IEEE Transactions on Fuzzy Systems 23.1 (2015): 152-163. https://arxiv.org/pdf/1711.11419.pdf

Liu, Derong, and Qinglai Wei. "Policy iteration adaptive dynamic programming algorithm for discrete-time nonlinear systems." IEEE Trans. Neural Netw. Learning Syst. 25.3 (2014): 621-634. doi=10.1.1.667.917

Wei, Qinglai, et al. "Multibattery optimal coordination control for home energy management systems via distributed iterative adaptive dynamic programming." IEEE Transactions on Industrial Electronics 62.7 (2015): 4203-4214.

Jiang, Yu, and Zhong-Ping Jiang. "Robust adaptive dynamic programming and feedback stabilization of nonlinear systems." IEEE Transactions on Neural Networks and Learning Systems 25.5 (2014): 882-893.

Jiang, Yu, and Zhong-Ping Jiang. "Global adaptive dynamic programming for continuous-time nonlinear systems." IEEE Transactions on Automatic Control 60.11 (2015): 2917-2929.

Yin, Jiateng, et al. "Energy-efficient metro train rescheduling with uncertain time-variant passenger demands: An approximate dynamic programming approach." Transportation Research Part B: Methodological 91 (2016): 178-210. http://or.nsfc.gov.cn/bitstream/00001903-5/489277/1/99879031.pdf

Tang, Yufei, et al. "Power system stability control for a wind farm based on adaptive dynamic programming." IEEE Transactions on Smart Grid 6.1 (2015) doi= 166-177. 10.1109

Tassa, Yuval, Nicolas Mansard, and Emo Todorov. "Control-limited differential dynamic programming." Robotics and Automation (ICRA), 2014 IEEE International Conference on. IEEE, 2014. https://homes.cs.washington.edu/~todorov/papers/TassaICRA14.pdf

Wei, Qinglai, and Derong Liu. "Adaptive dynamic programming for optimal tracking control of unknown nonlinear systems with application to coal gasification." IEEE Transactions on Automation Science and Engineering 11.4 (2014): 1020-1036. https://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=6656960

Wei, Qinglai, et al. "Finite-approximation-error-based discrete-time iterative adaptive dynamic programming." IEEE Transactions on Cybernetics 44.12 (2014): 2820-2833. doi= 10.1109


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