Optimal Control of a Discrete-Time Stochastic System with a Probabilistic Criterion and a Non-fixed Terminal Time

Azanov, Valentin M.

doi:10.1134/s0005117920120012

Cited by 1 publication

(4 citation statements)

References 13 publications

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“…3. An analysis of the current publications (e.g., see reviews in [14,[26][27][28][29][30][31][32][33][34][35]) suggests that optimal strategies are the principal instruments for containment of the epidemics of hepatitis C and the infection caused by the hepatitis B virus.…”

Section: State Of the Art And Motivation Using Sctmentioning

confidence: 99%

“…The consideration of the therapy as an optimal control problem has provided a number of successful theoretical and practical solutions [10,[24][25][26][27][28][29][30][31][32][33][34][35][36];…”

mentioning

confidence: 99%

“…The main trends in the research into biomedical systems are at the moment presented, on the one hand, by methods that allow studying the dynamic stability (equilibrium) properties [20,24,25,[31][32][33], the invariance, and the availability of periodic regimes applicable to such systems.…”

mentioning

confidence: 99%

“…On the other hand, there is an evolving trend associated with the formation of a purposeful external impact on an unstable biochemical process aimed at adding the required properties to the system [26][27][28][29][30][31][32][33][34][35]. The diversity of the methods used in the solution of this problem is dictated by the following: −The difference in the mathematical description (of the system of ODEs or difference equations) [17] and fractional reaction-diffusion modes [25]; −The level and types of the model uncertainties (deterministic [16,17] and stochastic [32]); −The quality criteria of a target system and the restrictions on the object and control parameters, etc.…”

mentioning

confidence: 99%

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

Kolesnikova,

Kustova

2023

Mathematics

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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.

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