Predictive management with all its errors and difficulties is still an effective means of providing an organizational and technical system with time to increase its readiness for changes in the situation. To formulate and solve the problem of optimal control of this process, the Fokker-Planck-Kolmogorov equation was used, which is the first approximation in the probabilistic description of random processes. To formulate the optimal control problem, the Letov criterion was modified, a coordinate-parametric approach was applied, and the obvious fact of an increase in management costs with a decrease in the time to improve the readiness of the organizational and technical system was taken into account in the form of the square of change rate in the probability density. The Euler-Ostrogradsky-Poisson equations are applied to the final Lagrangian. The resulting nonlinear equations were solved using the small parameter method. The study of the resulting solution proves that even with optimal control, the magnitude of control actions increases in proportion to the target value and duration of control (increasing the planning horizon), the increase occurs according to the cube of the exponential, that is, very slowly at the beginning of control and very sharply at the end, and a similar pattern of increase demonstrates the dependence of the control influences from the demand for management results, but it is expressed through hyperbolic functions.
1. Dyakonov N.A., Logunova O.S. Process control systems based on predictive analytics: design. Elektrotekhnicheskie sistemy i kompleksy = Electrotechnical Systems and Complexes. 2021;50(1):58–64. (In Russ.).
2. Novikov D.A. Theory of management of organizational systems. 4th ed., rev. and additional. Moscow, LENAND; 2022. 500 p. (In Russ.).
3. Burkov V.N., Irikov V.A. Models and methods of organizational management systems. Moscow, Science; 1994. 270 p. (In Russ.).
4. Lvovich A.I., Preobrazhensky A.P. Optimization of resource support at a given planning horizon of the organizational system development process using visual expert modeling. Modelirovanie, optimizatsiya i informatsionnye tekhnologii = Modeling, Optimization and Information Technology. 2022;10(3). URL: https://moitvivt.ru/ru/journal/pdf?id=1231 DOI: 10.26102/2310-6018/2022.38.3.015. (In Russ.).
5. Tikhonov A.N., Samarsky A.A. Equations of mathematical physics. Moscow, Science; 1977. 736 p. (In Russ.).
6. Akhmedyanova G.F., Pishchukhin A.M. Fundamentals of multi-level management in organizational and technical systems. Orenburg, Orenburg State University; 2020. 162 p. (In Russ.).
7. Pishchukhin A.M., Akhmedyanova G.F. Algorithms for synthesizing management solutions based on OLAP-technologies In: International Conference Information Technologies in Business and Industry 2018 – Enterprise Information Systems, 17–20 January 2018, Tomsk, Russia. Institute of Physics Publishing; 2018. p. 042001.
8. Zemlyakov S.D., Rutkovsky V.Yu. Functional controllability in adjustibility of coordinate-parametric control systems. Avtomatika i Telemekhanika. 1986;(2):21–30. (In Russ.).
9. Glumov V.M., Zemlyakov S.D., Rutkovsky V.Yu. Adaptive coordinate-parametric control for nonstationary plants: Certain results and development trends. Avtomatika i Telemekhanika. 1999;(6):100–116. (In Russ.).
10. Rutkovsky V.Yu., Zemlyakov S.D., Sukhanov V.M., Glumov V.M. New directions of adaptive coordinate-parametric control theory and applications. Problemy upravleniya = Control Sciences. 2003;(2):2–10. (In Russ.).
11. Letov A.M. Analytical design of controllers. I. Avtomatika i Telemekhanika. 1960;21(4):436–441. (In Russ.).
12. Letov A.M. Analytical design of controllers. II. Avtomatika i Telemekhanika. 1960;21(5):561–568. (In Russ.).
13. Letov A.M. Analytical design of controllers. III. Avtomatika i Telemekhanika. 1960;21(6):661–665. (In Russ.).
14. Letov A.M. Analytical design of controllers. IV. Avtomatika i Telemekhanika. 1961;22(4):425–435. (In Russ.).
15. Aleksandrov A.G. Optimal and adaptive systems. Moscow, Higher School; 1989. 263 p. (In Russ.).
16. Akhmedyanova G.F., Pishchukhin A.M. Optimal control of the production system based on a probabilistic criterion. Vestnik Cherepovetskogo gosudarstvennogo universiteta = Cherepovets State University Bulletin. 2022;110(5):7–19. (In Russ.).
17. Pishchukhin A.M. Probabilistic model of harmonization of the production process with the regional market. Vestnik Samarskogo gosudarstvennogo tekhnicheskogo universiteta. Seriya: Tekhnicheskie nauki = Vestnik of Samara State Technical University. Technical Sciences Series. 2019;61(1):20–33. (In Russ.).
18. Elsgolts L.E. Differential equations and calculus of variations. Moscow, Science; 1969. 426 p. (In Russ.).
19. Kamke E. Handbook of Ordinary Differential Equations. Moscow, Science; 1976. 576 p. (In Russ.).
Akhmedyanova Gulnara Fazulyanovna
Candidate of Pedagogical Sciences, Associate Professor
Scopus | ORCID | eLibrary |
Orenburg State University
Orenburg, the Russian Federation
