Overview of the recent research progress for stability and control on random nonlinear systems

Xi, Ruipeng; Zhang, Huaguang; Wang, Yingchun; Sun, Shaoxin

doi:10.1016/j.arcontrol.2022.03.005

Cited by 11 publications

(4 citation statements)

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“…In order to construct an immune system model of an organism, a class of nonlinear systems of ODEs with a delayed argument and a discontinuous right-hand part of the description is used. It is technically consistent with the concept of a "complex dynamic system" [39], with all the ensuing problems, since the results of research into stability analysis and designing control over nonlinear compound plants are far from being described as fruitful and systematic (e.g., see a review in [5]).…”

Section: State Of the Art And Motivation Using Sctmentioning

confidence: 54%

“…Here, we study the most interesting, from the practical viewpoint, uncertainties in the right-hand side of the description: non-random (piecewise-constant and harmonic functions) and random uncertainty (off-design conditions for the ADAR algorithm) (Figures [2][3][4][5][6]. The initial data correspond to the acute stage [17] (Table 1).…”

Section: Simulation Results For Acute Disease Stagementioning

confidence: 99%

“…There are algorithms for the analytical design of regulators based on adaptive control SCT and manifold invariance methods [12,37,44], which would meet the specified requirements in the cases of uncertainty in the parameters. 5. In [23,45,46], a survey of the current situation in immunology resulted in the following conclusion: a step towards an integration of systematic biology passes through "the epistemology of complexity", which relies on cybernetics and the interdisciplinary synergetic approach or self-organization theory and other works).…”

Section: State Of the Art And Motivation Using Sctmentioning

confidence: 99%

“…The importance of new control problem statements for bioengineering plants, which are characterized by poor formalizability, incompleteness of the information on biological processes, and instability of the limit states is supported by the object capacity to resist control) and the absence of a general approach to analyzing the free states of the nonlinear systems. Furthermore, it is extremely important to search for new properties of such objects, which might result from a control based on their physical features [1][2][3][4][5][6][7][8][9][10][11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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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Section: State Of the Art And Motivation Using Sctmentioning

confidence: 54%

Section: Simulation Results For Acute Disease Stagementioning

confidence: 99%