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Axioms
Special Issues
Mathematical Control and Applications
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Mathematical Control and Applications

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".

Deadline for manuscript submissions: closed (31 October 2022) | Viewed by 8177

Special Issue Editors

Dr. Francisco Javier Fernández Fernández

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Guest Editor
Estadística, Análisis Matemático y Optimización, Universidad de Santiago de Compostela, Facultad de Matemáticas, Lope Gómez de Marzoa, s/n. Campus Sur, CP/15782, Spain
Interests: partial differential equations; optimal control; differential equations; numerical resolution of partial differential equations; mathematical analysis
Prof. Dr. Alberto Cabada

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Guest Editor
Facultade de Matemáticas, Campus Vida, 15782 Santiago de Compostela, Galicia, Spain
Interests: ordinary differential equations; boundary value problems; Green's functions; comparison results; nonlinear analysis
Special Issues, Collections and Topics in MDPI journals
Dr. Miguel Ernesto Vazquez-Mendez

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Guest Editor
Matemática Aplicada, Universidade de Santiago de Compostela, Escola Politécnica Suprior de Enxeñaría, Benigno Ledo, s/n. Lugo, CP/27002, Spain
Interests: differential equations; partial differential equations; mathematical analysis

Special Issue Information

Dear Colleagues,

We would like to announce the launch of a Special Issue of Axioms, entitled “Mathematical Control and Applications”. We would like to provide the scientific community with an opportunity to share recent developments in the many branches of both theoretical and numerical studies in mathematics related to mathematical control and applications. For this Special Issue, we will consider research on topics in the following non-exhaustive list:

  • Mathematical analysis and the numerical resolution of optimal control problems in PDEs and ODEs;
  • Mathematical analysis and the numerical resolution of inverse problems in PDEs and ODEs;
  • Numerical optimization;
  • Automatic differentiation applied to the numerical resolution of optimization problems;
  • Data assimilation;
  • Other fields that have some intrinsic connections with control theory.

In addition to these topics, we will be open to further ideas for this Special Issue.

We hope that this initiative is of interest to you and encourage you to submit your current research for inclusion in the Special Issue.

Dr. Francisco Javier Fernández Fernández
Prof. Dr. Alberto Cabada
Dr. Miguel Ernesto Vazquez-Mendez
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Axioms is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • optimal control of PDEs and ODEs
  • inverse problems in PDEs and ODEs
  • numerical optimization
  • data assimilation
  • automatic differentiation

Published Papers (4 papers)

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Research

9 pages, 265 KiB  
Article
Application of the Averaging Method to the Optimal Control Problem of Non-Linear Differential Inclusions on the Finite Interval
by Tetiana Zhuk, Nina Kasimova and Anton Ryzhov
Axioms 2022, 11(11), 653; https://0-doi-org.brum.beds.ac.uk/10.3390/axioms11110653 - 17 Nov 2022
Cited by 1 | Viewed by 1017
Abstract
In this paper, we use the averaging method to find an approximate solution for the optimal control of non-linear differential inclusions with fast-oscillating coefficients on a finite time interval. Full article
(This article belongs to the Special Issue Mathematical Control and Applications)
13 pages, 8633 KiB  
Article
Optimal Location of Exit Doors for Efficient Evacuation of Crowds at Gathering Places
by Lino J. Alvarez-Vázquez, Néstor García-Chan, Aurea Martínez, Carmen Rodríguez and Miguel E. Vázquez-Méndez
Axioms 2022, 11(11), 592; https://0-doi-org.brum.beds.ac.uk/10.3390/axioms11110592 - 26 Oct 2022
Cited by 1 | Viewed by 1513
Abstract
This work deals with the optimal design for the location of the exit doors at meeting places (such as sports centers, public squares, street markets, transport stations, etc.) to guarantee a safer emergency evacuation in events of a sporting, social, entertainment or religious [...] Read more.
This work deals with the optimal design for the location of the exit doors at meeting places (such as sports centers, public squares, street markets, transport stations, etc.) to guarantee a safer emergency evacuation in events of a sporting, social, entertainment or religious type. This problem is stated as an optimal control problem of nonlinear partial differential equations, where the state system is a reformulation of the Hughes model (coupling the eikonal equation for a density-weighted walking velocity of pedestrians and the continuity equation for conservation of the pedestrian density), the control is the location of the exit doors at the domain boundary (subject to several geometric constraints), and the cost function is related to the evacuation rate. We provide a full numerical algorithm for solving the problem (a finite element technique for the discretization and a gradient-free procedure for the optimization), and show several numerical results for a realistic case. Full article
(This article belongs to the Special Issue Mathematical Control and Applications)
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21 pages, 1828 KiB  
Article
Source Identification of a Chemical Incident in an Urban Area
by Francisco J. Fernández and Miguel E. Vázquez-Méndez
Axioms 2021, 10(3), 177; https://0-doi-org.brum.beds.ac.uk/10.3390/axioms10030177 - 03 Aug 2021
Viewed by 1686
Abstract
This work deals aims to present a methodology for source identification of chemical incidents in urban areas. We propose an approximation of the problem within the framework of the optimal control theory and we provide an algorithm for its numerical resolution. Finally, we [...] Read more.
This work deals aims to present a methodology for source identification of chemical incidents in urban areas. We propose an approximation of the problem within the framework of the optimal control theory and we provide an algorithm for its numerical resolution. Finally, we analyze the validity of the algorithm in several academic situations. Full article
(This article belongs to the Special Issue Mathematical Control and Applications)
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24 pages, 1814 KiB  
Article
Optimal Control Analysis of Cholera Dynamics in the Presence of Asymptotic Transmission
by Emmanuel A. Bakare and Sarka Hoskova-Mayerova
Axioms 2021, 10(2), 60; https://0-doi-org.brum.beds.ac.uk/10.3390/axioms10020060 - 12 Apr 2021
Cited by 13 | Viewed by 2758
Abstract
Many mathematical models have explored the dynamics of cholera but none have been used to predict the optimal strategies of the three control interventions (the use of hygiene promotion and social mobilization; the use of treatment by drug/oral re-hydration solution; and the use [...] Read more.
Many mathematical models have explored the dynamics of cholera but none have been used to predict the optimal strategies of the three control interventions (the use of hygiene promotion and social mobilization; the use of treatment by drug/oral re-hydration solution; and the use of safe water, hygiene, and sanitation). The goal here is to develop (deterministic and stochastic) mathematical models of cholera transmission and control dynamics, with the aim of investigating the effect of the three control interventions against cholera transmission in order to find optimal control strategies. The reproduction number Rp was obtained through the next generation matrix method and sensitivity and elasticity analysis were performed. The global stability of the equilibrium was obtained using the Lyapunov functional. Optimal control theory was applied to investigate the optimal control strategies for controlling the spread of cholera using the combination of control interventions. The Pontryagin’s maximum principle was used to characterize the optimal levels of combined control interventions. The models were validated using numerical experiments and sensitivity analysis was done. Optimal control theory showed that the combinations of the control intervention influenced disease progression. The characterisation of the optimal levels of the multiple control interventions showed the means for minimizing cholera transmission, mortality, and morbidity in finite time. The numerical experiments showed that there are fluctuations and noise due to its dependence on the corresponding population size and that the optimal control strategies to effectively control cholera transmission, mortality, and morbidity was through the combinations of all three control interventions. The developed models achieved the reduction, control, and/or elimination of cholera through incorporating multiple control interventions. Full article
(This article belongs to the Special Issue Mathematical Control and Applications)
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