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International Theoretical Science Journal
Volume 62 >>> № 4 JULY — AUGUST 2026
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DOI 10.34229/KCA2522-9664.26.4.12
UDC 517.9:681.51:519.8

D.I. Symonov
V.M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine,
Kyiv, Ukraine,  denys.symonov@gmail.com


AN INTEGRAL ENTROPY INDICATOR FOR THE CONTROLLABILITY
OF COMPLEX SYSTEM EVOLUTION

Abstract. The study proposes a formalized approach to analyzing the controllability of the evolution of complex multi-agent systems based on an integral entropy-based indicator of the risk of loss of controllability. A multilevel model of multi-agent system dynamics is constructed that integrates the microdynamics of agents, the mesostructural organization of the interaction network, and macro-level invariants governing system evolution. At the macro level, an integral indicator is introduced and formulated as a composition of barrier components that reflect variability of macrodynamics, the risk of violation of the invariance of the admissible state domain, and the loss of spectral stability of the system regime. This construction enables quantitative assessment of the proximity of the system trajectory to the boundary of controllability loss. The predictive properties of the indicator are examined through a series of numerical experiments employing scenarios of both stable and critical evolution of the multi-agent system. Results of Monte Carlo validation demonstrate the capability of the proposed approach to detect pre-critical regimes of system dynamics and to distinguish between stable and unstable evolutionary regimes in complex multi-agent systems.

Keywords: integral indicator of evolutionary controllability, entropy, multi-agent systems, evolution of complex systems, macrodynamics, barrier functions, early detection of critical states.


full text

REFERENCES

    1. Dahling S., Razik L., Monti A. Enabling scalable and fault-tolerant multi-agent systems by utilizing cloud-native computing. Autonomous Agents and Multi-Agent Systems. 2021. Vol. 35, N 10. https://doi.org/10.1007/s10458-020-09489-0.
    2. Zargayouna M. On the use of the multi-agent environment for mobility applications. Future Internet. 2022. Vol. 14, N 5. Article number 132. https://doi.org/10.3390/fi14050132.
    3. Xu L., Mak S., Schoepf S., Ostroumov M., Brintrup A. Multi-agent digital twinning for collaborative logistics: Framework and implementation. Journal of Industrial Information Integration. 2023. Vol. 45. Article number 100799. https://doi.org/10.1016/j.jii.2025.100799.
    4. Knopov P.S. Optimization and identification of stochastic systems. Cybernetics and Systems Analysis. 2023. Vol. 59, N 3. P. 375–384. https://doi.org/10.1007/s10559-023-00572-4.
    5. Chikrii A.A., Rappoport I.S. Strategies for quasi-parallel convergence and motion camouflage in game control problems with non-fixed time. Cybernetics and Systems Analysis. 2025. Vol. 61, N 5. P. 772–781. https://doi.org/10.1007/s10559-025-00810-x.
    6. Mehdizadeh M., Nordfjaern T., Klckner C. A systematic review of the agent-based modelling/simulation paradigm in mobility transition. Technological Forecasting and Social Change. 2022. Vol. 184. Article number 122011. https://doi.org/10.1016/j.techfore.2022.122011.
    7. Mazzetto S. Interdisciplinary perspectives on agent-based modeling in the architecture, engineering, and construction industry: A comprehensive review. Buildings. 2024. Vol. 14, N 11. Article number 3480. https://doi.org/10.3390/buildings14113480.
    8. Brugiere A., Nguyen-Ngoc D., Drogoul A. Handling multiple levels in agent-based models of complex socio-environmental systems: A comprehensive review. Frontiers in Applied Mathematics and Statistics. 2022. Vol. 8. Article number 1020353. https://doi.org/10.3389/fams.2022.1020353.
    9. Nawaz S., Saleem M., Kusmartsev F.V., Anjum D.H. Major role of multiscale entropy evolution in complex systems and data science. Entropy (Basel). 2024. Vol. 26, N 4. Article number 330. https://doi.org/10.3390/e26040330.
    10. Gupal A.M., Vagis O.A. Incompleteness theorem for computable problems. Cybernetics and Systems Analysis. 2024. Vol. 60, N 5. P. 696–699. https://doi.org/10.1007/s10559-024-00707-1.
    11. Albrecht S.V., Christianos F., Schfer L. Multi-agent reinforcement learning: Foundations and modern approaches. Cambridge, MA: MIT Press, 2024. 544 p.
    12. Palagin O.V., Symonov D.I. Formalized model of attitude formation as a tool for analyzing behavioral patterns. Cybernetics and Systems Analysis. 2025. Vol. 61, N 5. P. 705–713. https://doi.org/10.1007/s10559-025-00804-9.
    13. Palagin O., Symonov D., Symonova O. Agent behavior prediction based on a dynamic cognitive model. Cybernetics and Systems Analysis. 2026. Vol. 62, N 2. P. 181–195. https://doi.org/10.1007/s10559-026-00856-5.
    14. Zhang D., Yuan Q., Meng L. et al. Reinforcement learning for single-agent to multi-agent systems: From basic theory to industrial application progress, a survey. Artificial Intelligence Review. 2026. Vol. 59. Article number 46. https://doi.org/10.1007/s10462-025-11439-9.
    15. Sergienko I.V., Shylo V.P., Roshchyn V.O. Algorithm unions for solving discrete optimization problems. Cybernetics and Systems Analysis. 2023. Vol. 59, N 5. P. 753–762. https://doi.org/10.1007/s10559-023-00611-0.
    16. Allday J., Hands S. Introduction to entropy: The way of the world. Boca Raton: CRC Press, 2025. 358 p.
    17. Schaffler S. Mathematics of information. Theory and Applications of Shannon–Wiener Information. Berlin, Heidelberg: Springer, 2024. 150 p. https://doi.org/10.1007/978-3-662-69102-1.
    18. Campbell C., Hoeller T. Postdigital complexity science. Jandriс P. (Eds.). Encyclopedia of Postdigital Science and Education. Cham: Springer, 2025. P. 1–9. https://doi.org/10.1007/978-3-031-35469-4_94-1.
    19. Symonov D., Palagin O., Symonov Y., Zaika B. Optimisation of training samples with KLE and mutual information. Proceedings of the Eighth International Workshop on Computer Modeling and Intelligent Systems (CMIS 2025). CEUR Workshop Proceedings. 2025. Vol. 3988. P. 296–306. https://ceur-ws.org/Vol-3988/paper23.pdf.



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