scholarly journals Research of the Optimal Control Problem for One Mathematical Model of the Sobolev Type

2021 ◽  
Vol 14 (4) ◽  
pp. 36-45
Author(s):  
K.V. Perevozchikova ◽  
◽  
N.A. Manakova
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Sobolev Type

scholarly journals Kendali Optimal Pada Model Penyebaran Penyakit Difteri dengan Tingkat Imunitas Alami Pada Individu Terpapar

2021 ◽  
Vol 18 (1) ◽  
pp. 1-10
Author(s):  
N Izzati ◽  
A Andriani
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Mortality Rate ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Management Strategies ◽  
Immunization Coverage ◽  
Natural Immunity ◽  
Exposed Population ◽  
Number Of Individuals

Indonesia is one of the countries where has not been free from diphtheria outbreak. During 2017-2019, there were 2870 diphtheria cases with 96 deaths. With the mortality rate 5-20%, makes studies regarding diphtheria prevention and management strategies become important to do. In this study, a SEIQR mathematical model was constructed by considering the factor of natural immunity rate in exposed individuals. Then, by considering the complete basic immunization coverage and the proportion of the number of individuals with natural immunity rate as control variables, the optimal control problem is formulated to minimize the number of infected poopulation. Optimal control using DOTcvpSB toolbox obtained that the number of exposed population in the model decreased from 4.9% to 0.75%, and the number of infected population decreased from 3.1% to 0.32%.

Symmetric Control Systems

2021 ◽  
pp. 37-51
Author(s):  
A.I. Diveev ◽  
E.A. Sofronova
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Control Systems ◽  
Control Object ◽  
Terminal State ◽  
Initial State ◽  
Phase Constraints ◽  
The Mathematical Model

The paper focuses on the properties of symmetric control systems, whose distinctive feature is that the solution of the optimal control problem for an object, the mathematical model of which belongs to the class of symmetric control systems, leads to the solution of two problems. The first optimal control problem is the initial one; the result of its solution is a function that ensures the optimal movement of the object from the initial state to the terminal one. In the second problem, the terminal state is the initial state, and the initial state is the terminal state. The complexity of the problem being solved is due to the increase in dimension when the models of all objects of the group are included in the mathematical model of the object, as well as the emerging dynamic phase constraints. The presence of phase constraints in some cases leads to the target functional having several local extrema. A theorem is proved that under certain conditions the functional is not unimodal when controlling a group of objects belonging to the class of symmetric systems. A numerical example of solving the optimal control problem with phase constraints by the Adam gradient method and the evolutionary particle swarm method is given. In the example, a group of two symmetrical objects is used as a control object

scholarly journals Optimal control for a mathematical model for chemotherapy with pharmacometrics

2020 ◽  
Vol 15 ◽  
pp. 69
Author(s):  
Maciej Leszczyński ◽  
Urszula Ledzewicz ◽  
Heinz Schättler
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Cancer Chemotherapy ◽  
Drug Effects ◽  
Optimal Controls ◽  
Angiogenic Therapy ◽  
Single Drug ◽  
Qualitative Changes

An optimal control problem for an abstract mathematical model for cancer chemotherapy is considered. The dynamics is for a single drug and includes pharmacodynamic (PD) and pharmacokinetic (PK) models. The aim is to point out qualitative changes in the structures of optimal controls that occur as these pharmacometric models are varied. This concerns (i) changes in the PD-model for the effectiveness of the drug (e.g., between a linear log-kill term and a non-linear Michaelis-Menten type Emax-model) and (ii) the question how the incorporation of a mathematical model for the pharmacokinetics of the drug effects optimal controls. The general results will be illustrated and discussed in the framework of a mathematical model for anti-angiogenic therapy.

scholarly journals Validation of a Mathematical Model of Cancer Incorporating Spontaneous and Induced Evolution to Drug Resistance

2019 ◽  
Author(s):  
Jana L. Gevertz ◽  
James M. Greene ◽  
Eduardo D. Sontag
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Optimal Control ◽  
Drug Resistance ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Additional Data ◽  
Fitting In

AbstractThis paper continues the study of a model which was introduced in earlier work by the authors to study spontaneous and induced evolution to drug resistance under chemotherapy. The model is fit to existing experimental data, and is then validated on additional data that had not been used when fitting. In addition, an optimal control problem is studied numerically.

scholarly journals An optimal control problem applied to a wastewater treatment plant

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
M. Teresa T. Monteiro ◽  
Isabel Espírito Santo ◽  
Helena Sofia Rodrigues
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Wastewater Treatment ◽  
Optimal Control Problem ◽  
Dissolved Oxygen ◽  
Activated Sludge ◽  
Control Problem ◽  
Control Variable ◽  
Treatment Plant ◽  
Domestic Effluent

<p style='text-indent:20px;'>This paper aims to present a mathematical model that describes the operation of an activated sludge system during one day. Such system is used in the majority of wastewater treatment plants and depends strongly on the dissolved oxygen, since it is a biological treatment. To guarantee the appropriate amount of dissolved oxygen, expensive aeration strategies are demanded, leading to high costs in terms of energy consumption. It was considered a typical domestic effluent as the wastewater to test the mathematical model and it was used the ASM1 to describe the activated sludge behaviour. An optimal control problem was formulated whose cost functional considers the trade-off between the minimization of the control variable herein considered (the dissolved oxygen) and the quality index that is the amount of pollution. The optimal control problem is treated as a nonlinear optimization problem after discretization by direct methods. The problem was then coded in the AMPL programming language in order to carry out numerical simulations using the NLP solver IPOPT from NEOS Server.</p>

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