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Application of a Stochastic Extension of the Analytical Design of Aggregated Regulators to a Multidimensional Biomedical Object

Author

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  • Svetlana Kolesnikova

    (Department of Computer Technologies and Software Engineering, Institute of Computing Systems and Programming, Saint Petersburg State University of Aerospace Instrumentation, Saint Petersburg 190000, Russia)

  • Ekaterina Kustova

    (Department of Computer Technologies and Software Engineering, Institute of Computing Systems and Programming, Saint Petersburg State University of Aerospace Instrumentation, Saint Petersburg 190000, Russia)

Abstract

The results of the application of the methods of the synergetic control theory to a high-dimensional immunology object with uncertainty in its descriptions are reported. The control here is the therapy treated as a problem for constructing an optimal cure program. The control object is presented in continuous and discrete forms, i.e., mathematical models given by a system of ordinary differential equations with a bounded disturbance and a system of stochastic difference equations, respectively. Two algorithms for deriving robust regulators applicable to a 10-dimensional nonlinear multi-loop system with unstable limit states, which models an immune response to the hepatitis B infection, are obtained. Analytical control design for a continuous model relies on the method of nonlinear adaptation on the target manifold. The second algorithm represents a stochastic extension of the method of analytical design of aggregated discrete regulators minimizing the variance of the target macro variable. The numerical simulation of the developed control systems indicates the performance of the designed control algorithms. The results of this study can be used as a component part of the mathematical tools of expert systems and decision support systems.

Suggested Citation

  • Svetlana Kolesnikova & Ekaterina Kustova, 2023. "Application of a Stochastic Extension of the Analytical Design of Aggregated Regulators to a Multidimensional Biomedical Object," Mathematics, MDPI, vol. 11(21), pages 1-20, October.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:21:p:4484-:d:1270592
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    References listed on IDEAS

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    1. de Souza, Elder & Lyra, Marcelo & Gleria, Iram, 2009. "Critical bifurcations and chaos in a delayed nonlinear model for the immune response," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2494-2501.
    2. Kumar, Anuj & Srivastava, Prashant K. & Dong, Yueping & Takeuchi, Yasuhiro, 2020. "Optimal control of infectious disease: Information-induced vaccination and limited treatment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 542(C).
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