Русская версия
ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

About History Editorial Page Addresses Scope Editorial Staff Submission Review For Authors Publication Ethics Issues Русская версия

Modeling and Stabilization of an Irregular Pricing Mechanism on a Network of Local Markets

Author(s):

Tatyana Anatolyevna Alexeeva

HSE University,
Saint Petersburg School of Physics, Mathematics, and Computer Science,
Kantemirovskaya Street, 3
St Petersburg, 194100, Russia
Cand. of Physical and Mathematical Sciences

talekseeva@hse.ru

Nikolay Vladimirovich Kuznetsov

Doctor of physico-mathematical sciences, Head of the Department of Applied Cybernetics, St. Petersburg State University,
Head of the Laboratory of Information and Control Systems of the Institute for Problems in
Mechanical Engineering of the Russian Academy of Sciences (IPMash RAS)

nkuznetsov239@mail.ru

Timur Nazirovich Mokaev

St. Petersburg State University,
Faculty of Mathematics and Mechanics,
Peterhof,
St. Petersburg

tim.mokaev@gmail.com

Konstantin Mikhailovich Posudin

St. Petersburg State University,
Faculty of Mathematics and Mechanics,
Department of Applied Cybernetics,
Peterhof,
St. Petersburg

kposudin@gmail.com

Abstract:

The accuracy of forecasting the expected values of economic indicators under conditions of irregular dynamics has a key role in taking optimal management decision-making. The solution of this current and complex task requires the use of modern artificial intelligence technologies, the wide introduction of which into the economy is aimed at by the Federal project ``Artificial Intelligence''. We demonstrate the effectiveness of combining artificial intelligence technologies and classical methods of mathematical control to detect irregular dynamics in the pricing mechanism and stabilize the revealed irregular mode through a small control action using a pricing model in the market of short-term goods as an example.

Keywords

References:

  1. Kantorovich L. V. Mathematics in Economics: Achievements, Difficulties, Perspectives. Nobel Lectures and 1989 Survey of Members (Dec., 1989). The American Economic Review, 1989, 79 (6), 18-22
  2. Kantorovich L. V. Matematicheskie metodi organizacii i planirovaniya proizvodstva [Mathematical methods of organization and planning of production]. Leningrad, Leningrad St. Univ. Publ., 1939. 68 p
  3. Kantorovich L. V. Ekonomicheskij raschet nailuchshego ispol'zovaniya resursov [Economic calculation of the best use of resources]. Moscow, Akademiya nauk SSSR Publ., 1959. 344 p
  4. Buhvalov A. V. L. V. Kantorovich and economic and mathematical modelling: synthesis of reality, mathematics and economics [Kantorovich i ekonomiko-matematicheskoe modelirovanie: sintez real'nosti, matematiki i ekonomiki. Rossijskij zhurnal menedzhmenta]. Rossijskij zhurnal menedzhmenta, 2012; 10(3):3‑ 30. (In Russ. )
  5. Leonid Vital'evich Kantorovich: matematika, menedzhment, informatika. Eds. G. A. Leonov, V. S. Kat'kalo, A. V. Buhvalov [Leonid Vitalievich Kantorovich: mathematics, management, computer science]. St. Petersburg, «Vysshaya shkola menedzhmenta» Publ., 2009. 575 p
  6. Vershik A. M., Kutateladze S. S., Novikov S. P. Leonid Vitalievich Kantorovich (on the occasion of his 100th birthday) [Leonid Vital'evich Kantorovich (k 100-letiyu so dnya rozhdeniya)]. Uspekhi matematicheskih nauk, 2012; 67:3(405), 185‑ 191. (In Russ. )
  7. Kantorovich L. V. On carrying out numerical and analytical calculations on machines with program control [O provedenii chislennyh i analiticheskih vychislenij na mashinah s programmnym upravleniem]. Izv. AN Arm. SSR, 1957; 10(2):3‑ 16. (In Russ. )
  8. Kantorovich L. V. On some new approaches to computational methods and processing of observations [O nekotoryh novyh podhodah k vychislitel'nym metodam i obrabotke nablyudenij]. Sib. matem. zhurn. , 1962; 3(5):701-709. (In Russ. )
  9. Daugavet O. K., Romanovskij I. V. On the activities and works of L. V. Kantorovich in the field of programming [O deyatel'nosti i rabotah L. V. Kantorovicha v oblasti programmirovaniya]. Zhurnal Novoj ekonomicheskoj associacii, 2012; 1(13):185‑ 190. (In Russ. )
  10. Kuznetsov N. Theory of hidden oscillations and stability of control systems. Journal of Computer and Systems Sciences International, 2020, 59, 647‑ 668
  11. Parkes D., Wellman M. Economic reasoning and artificial intelligence, Science, 349(6245), 2015, 267‑ 272
  12. Maliar L., Maliar S., Winant P. Deep learning for solving dynamic economic models, Journal of Monetary Economics, 2021; 122:76‑ 101
  13. Barnett W., Bella G., Ghosh T., Mattana P., Venturi B. Shilnikov chaos, low interest rates, and New Keynesian macroeconomics. Journal of Economic Dynamics and Control, 2022; 134:art. num. 104291
  14. Galizia D. Saddle cycles: Solving rational expectations models featuring limit cycles (or chaos) using perturbation methods, Quantitative Economics, 2021; 12(3):869‑ 901
  15. Beaudry P., Galizia D., Portier F. Putting the cycle back into business cycle analysis. American Economic Review, 2020; 110 (1):1‑ 47
  16. Alexeeva T., Kuznetsov N., Mokaev T. Study of irregular dynamics in an economic model: attractor localization and Lyapunov exponents. Chaos, Solitons & Fractals, 2021; 152:art. num. 111365
  17. Alexeeva T., Mokaev T., Polshchikova I. Dynamics of monetary and fiscal policy in a New Keynesian model in continuous time. Differencialnie Uravnenia i Protsesy Upravlenia/Differential Equations and Control Processes, 2020, no. 4
  18. Aliber R. Z., Kindleberge C. P. Manias, Panics, and Crashes: A History of Financial Crises, Palgrave Macmillan UK, 2015. 435 p
  19. Taleb N. N. The Black Swan: The Impact of the Highly Improbable (The Incerto Collection). Random House and Penguin, 2007. 400 p
  20. Alexeeva T., Barnett W., Kuznetsov N., Mokaev T. Time delay control for stabilization of the Shapovalov mid-size firm model. IFAC-PapersOnLine, 2020; 53(2):16971‑ 16976
  21. Alexeeva T. A., Diep Q. -B., Kuznetsov N. V., Zelinka I. Forecasting and stabilizing chaotic regimes in two macroeconomic models via artificial intelligence technologies and control methods. Chaos, Solitons & Fractals, 2023; 170:art. num. 113377
  22. Alekseeva T. A., Belyaev A. Yu., Kuznecov N. V., Mokaev T. N. [Commodity price forecasting and chaos control in network markets: nonlinear analysis and artificial intelligence technologies]. Materiali 15-i multikonferencii po problemam upravleniya “Matematicheskaya teoriya upravleniya i ee prilojeniya (MTUIP-2022)”. St. Petersburg, AO «Koncern “CNII “Elektropribor” [Proc. Multiconf. “Mathematical control theory and its application-2022”], 2022, pp. 225-228 (In Russian)
  23. Ikemoto J., Ushio T. Continuous deep Q-learning with a simulator for stabilization of uncertain discrete-time systems, Nonlinear Theory and Its Applications, IEICE, 12 (4), 2021, 738‑ 757
  24. Pyragas K. Continuous control of chaos by self-controlling feedback. Physis letters A, 1992; 170(6):421‑ 428
  25. Storn R., Price K. Differential evolution ‑ a simple and efficient heuristic for global optimization over continuous spaces. Journal of global optimization, 1997; 11(4):341‑ 359
  26. Chow S. N. Lattice Dynamical Systems. In: Macki, J. W., Zecca, P. (eds) Dynamical Systems. Lecture Notes in Mathematics. Springer, 2003, no. 1822, pp. 1‑ 102
  27. Henon M. A two-dimensional mapping with a strange attractor. Communications in Mathematical Physics, 1976; 50:69‑ 77
  28. Sutton R., Barto A. Introduction to Reinforcement Learning. Cambridge: MIT press, 1998. 322 p
  29. Gu S., Lillicrap T., Sutskever I., Levine S. Continuous Deep Q-Learning with Model-Based Acceleration. ICML'16: Proceedings of the 33rd International Conference on International Conference on Machine Learning, 2016; 48:2829‑ 2838
  30. Dudkowski D., Jafari S., Kapitaniak T., Kuznetsov N., Leonov G., Prasad A. Hidden attractors in dynamical systems. Physics Reports, 2016; 637:1‑ 50
  31. Prasad A. Existence of perpetual points in nonlinear dynamical systems and its applications. International Journal of Bifurcation and Chaos, 2015; 25(2):art. num. 153005
  32. Leonov G., Kuznetsov N. Hidden attractors in dynamical systems. From hidden oscillations in Hilbert-Kolmogorov, Aizerman, and Kalman problems to hidden chaotic attractors in Chua circuits. International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 2013; 23(1):art. num. 1330002
  33. Kuznetsov N., Leonov G., Mokaev T., Prasad A., Shrimali M. Finite-time Lyapunov dimension and hidden attractor of the Rabinovich system. Nonlinear Dynamics, 2018; 92(2):267‑ 285
  34. Kuznetsov N., Mokaev T., Kuznetsova O., Kudryashova E. The Lorenz system: hidden boundary of practical stability and the Lyapunov dimension. Nonlinear Dynamics, 2020; 102:713‑ 732
  35. Kuznetsov N., Mokaev T., Ponomarenko V., Seleznev E., Stankevich N., Chua L. Hidden attractors in Chua circuit: mathematical theory meets physical experiments. Nonlinear Dynamics, 2023; 111:5859‑ 5887
  36. Dudkowski D., Prasad A., Kapitaniak T. Perpetual points and periodic perpetual loci in maps. Chaos, 2016; 26:art. num. 103103

Full text (pdf)