Entropy aspect of optimization models for the design reliability of automated control cystems

The paper studies and analyzes the formal definition and substantive interpretation of an information-based assessment of the design reliability of automated control systems for large water transport facilities with distributed locations, such as ports, shipping companies, and regional networks of regulated inland waterways. The concept of “project entropy” and the related measure of information uncertainty are introduced in connection with optimization mathematical models describing the interaction between reliability and cost indicators of automated control systems. The paper reviews and analyzes publications dealing with the transfer of the probabilistic-theoretical definition of entropy of a finite scheme of a complete system of events, proposed by Shannon and Khinchin, to models of the functioning of technical and techno-economic systems, as well as publications on the relationship between project entropy and Kolmogorov information in the context of optimization aspects of design. The concept of design entropy is formulated with regard to mathematical models for optimizing design reliability at the development stage. A method is described for constructing an entropy estimate for the preliminary design of an automated control system for a water transport production-and-economic system, with hardware, software, and data storage subsystems identified within it, as previously discussed in the first author’s publications. In this paper, entropy is treated as a measure of information lost when a project deviates from an optimal or quasi-optimal variant. The reliability factors used as arguments of the objective function include technical indicators, such as mean time between failures and restoration time, as well as economic indicators, including the initial cost of hardware and the cost of restoration, which are relevant under the limited overall budget of an automated control system throughout its life cycle. It is shown that the entropy of the optimal plan of an extremal problem on a discrete finite feasible domain is equal to the logarithm of the domain cardinality. The conclusion is drawn that the optimal plan is characterized by maximum uncertainty and the most complete use of the information represented by the feasible domain of constraints.

1. Khinchin, A. Ya. "Ponyatie entropii v teorii veroyatnostey." Uspekhi matematicheskikh nauk 8.3 (55) (1953): 3–20.

2. Sokolov, V. K. "O svyazi informatsii i ekonomicheskogo effekta ASDU." Izvestiya AN SSSR. Energetika i transport 4 (1989): 31–37.

3. Blagin, A. V., L. V. Blagina, I. G. Popova and Yu. V. Sakharova. "Entropy analysis of complex systems as a tool of engineering activity." Ingineering Journal of Don 4(51) (2018): 16.

4. Dulesov, A. S., N. S. Fedorenko and A. V. Bayshev. "Estimation of the possibilities of measuring the amount of entropy in the analysis of the reliability of technical systems." Vestnik Khakasskogo gosudarstvennogo universiteta imeni N.F. Katanova 1(35) (2021): 43–48.

5. Litskevich, A. P., B. N. Lobov and S. A. Litskevich. "Entropic approach to the analysis of reliability technical objects." Transport Business in Russia 3 (2017): 107–110.

6. Bondar', A., S. Bushuev and S. Onischenko. "Project management fighting against entropy of the organization." Scientific Journal of Astana IT University 2.2 (2020): 60–70. DOI: 10.37943/AITU.2020.88.62.006.

7. Kokin, A. V. and T. U. Albakova. "The entropy of complexity and administration complexity." State and Municipal Management. Scholar Notes 1 (2012): 15–28.

8. Azarenkova, N. V. "Mechanisms of regulating entropy in corporate information systems." Izvestiya of Altai State University 1-2(77) (2013): 063–065.ы

9. Chertkov, A. A., V. Yu. Ivanyuk and Ya. N. Kask. "Evaluation of diagnostic parameters of complex systems in water transport in terms of the entropy approach." Vestnik of Astrakhan State Technical University. Series: Management, Computer Science and Informatics 3 (2023): 29–36. DOI: 10.24143/2072-9502-2023-3-29-36.

10. Karasev, V. V. "Entropy of complex systems as a measure of risk." Imitatsionnoe modelirovanie. Teoriya i praktika (IMMOD-2025) : Trudy konferentsii, Sankt-Peterburg, 15–17 oktyabrya 2025 goda Sankt-Peterburg: AO «TsTSS», 2025: 821–832.

11. Rybak, A. T., S. V. Teplyakova, A. V. Ol'shevskaya and A. S. Prutskov. "A method for monitoring the reliability of technical systems by identifying the entropy of the causes of their failures." Advanced Engineering Research (Rostov-on-Don) 25.2 (2025): 112–119. DOI: 10.23947/2687-1653-2025-25-2-112-119.

12. Dulesov, A. S. and N. S. Fedorenko. "Entropy-probabilistic event tree analysis." Scientific and Technical Volga Region Bulletin 6 (2023): 152–157.

13. Dulesov, A. S., N. V. Dulesova and N. S. Fedorenko. "Applied significance of a. hinchin entropy in structural reliability analysis of electricity distribution networks." Scientific and Technical Volga Region Bulletin 9 (2023): 81–85.

14. Korotkov, V. V. "Methodology for forming an integral assessment of the reliability of automated control systems of transport infrastructure at the design stage." Vestnik gosudarstvennogo universiteta morskogo i rechnogo flota imeni admirala S.O. Makarova 17.3 (2025): 449–458. DOI: 10.21821/2309-5180-2025-17-3-449-458.

15. Korotkov, V. V. "Matematicheskie modeli proektnoy optimizatsii apparatnogo kontura ASU. ." Nauka i tekhnika transporta 1 (2026): 20–29.

16. Bayyr, D. B., A. S. Dulesov and E. V. Pupkova. "Possibilities of entropy application in the analysis of data scattering about the state of technical system." Herald of Gstou. Engineering Sciences 21.2(40) (2025): 25–33.

17. Bayyr, D. B. and A. S. Dulesov. "Analysis of technical systems based on alfred renyi entropy." Vserossiyskiy nauchnyy zhurnal "Voprosy prava" 2 (2024): 179–181.