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

Svetlana Kolesnikova () and Ekaterina Kustova
Additional contact information
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

Mathematics, 2023, vol. 11, issue 21, 1-20

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.

Keywords: object of immunology; discrete stochastic system; system invariant; macro variable; variational problem; biomedical systems (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/21/4484/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/21/4484/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:11:y:2023:i:21:p:4484-:d:1270592

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().