Advances in Numerical Methods for Optimal Control Problems

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E2: Control Theory and Mechanics".

Deadline for manuscript submissions: 31 October 2025 | Viewed by 923

Special Issue Editors


E-Mail Website
Guest Editor
Department of Mathematics and Statistics, College of Arts & Sciences, University of North Florida, Jacksonville, FL, USA
Interests: finite element method; computational fluid dynamics; numerical analysis; finite element analysis; numerical mathematics; FSI; scientific computing; applied mathematics engineering, applied and computational mathematics; numerical simulation

E-Mail Website
Guest Editor
Department of Systems and Naval Mechantronics Engineering, National Cheng Kung University, No.1, University Rd., East District, Tainan City 701, Taiwan
Interests: numerical method; optimal control; thermal system analysis; inverse problems

Special Issue Information

Dear Colleagues,

Optimal control problems have found applications in numerous fields, such as aerospace, process control, and economics, and they continue to be a research area of great interest to many professionals. The goal of optimal control problems is to determine control and state trajectories for a dynamical system over a period of time such that an objective functional is optimized, for example, to send a rocket to the moon with minimal fuel consumption or to find the time-dependent optimal temperature inside a sterilizing chamber for canned food. 

However, practical optimal control problems are usually too complex to solve analytically. Thus, many numerical algorithms have been developed and implemented to find approximate solutions to such problems.

This Special Issue aims to explore the most recent results in numerical methods for optimal control problems in both theoretical analysis and computational implementations.

Prof. Dr. Kening Wang
Prof. Dr. Cheng-Hung Huang
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. Mathematics is an international peer-reviewed open access semimonthly 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 2600 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
  • dynamical systems
  • differential equations
  • numerical analysis
  • computational implementation

Benefits of Publishing in a Special Issue

  • Ease of navigation: Grouping papers by topic helps scholars navigate broad scope journals more efficiently.
  • Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.
  • Expansion of research network: Special Issues facilitate connections among authors, fostering scientific collaborations.
  • External promotion: Articles in Special Issues are often promoted through the journal's social media, increasing their visibility.
  • e-Book format: Special Issues with more than 10 articles can be published as dedicated e-books, ensuring wide and rapid dissemination.

Further information on MDPI's Special Issue policies can be found here.

Published Papers (1 paper)

Order results
Result details
Select all
Export citation of selected articles as:

Research

24 pages, 1063 KiB  
Article
Optimal Control of Heat Equation by Coupling FVM and FEM Codes
by Samuele Baldini, Giacomo Barbi, Antonio Cervone, Federico Giangolini, Sandro Manservisi and Lucia Sirotti
Mathematics 2025, 13(2), 238; https://doi.org/10.3390/math13020238 - 12 Jan 2025
Cited by 1 | Viewed by 604
Abstract
In this paper, the optimal control theory is applied to a temperature optimization problem by coupling finite element and finite volume codes. The optimality system is split into the state and adjoint system. The direct problem is solved by the widely adopted finite [...] Read more.
In this paper, the optimal control theory is applied to a temperature optimization problem by coupling finite element and finite volume codes. The optimality system is split into the state and adjoint system. The direct problem is solved by the widely adopted finite volume OpenFOAM code and the adjoint-control equation using a variational formulation of the problem with the in-house finite element FEMuS code. The variational formulation of the problem is the natural framework for accurately capturing the control correction while OpenFOAM guarantees the accuracy of the state solution. This coupling is facilitated through the open-source MED and MEDCoupling libraries of the SALOME platform. The code coupling is implemented with the MED libraries and additional routines added in the FEMuS and OpenFOAM codes. We demonstrate the accuracy, robustness, and performance of the proposed approach with examples targeting different objectives using distributed and boundary controls in each case. Full article
(This article belongs to the Special Issue Advances in Numerical Methods for Optimal Control Problems)
Show Figures

Figure 1

Back to TopTop