Next Article in Journal
General Odd and Even Central Factorial Polynomial Sequences
Previous Article in Journal
The Parabola: Section of a Cone or Locus of Points of a Plane? Tips for Teaching of Geometry from Some Writings by Mydorge and Wallis
 
 
Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
Journals
Mathematics
Volume 10
Issue 6
10.3390/math10060977
mathematics-logo
Submit to this Journal Review for this Journal Propose a Special Issue
► Article Menu

Article Menu

share Share announcement Help format_quote Cite question_answer Discuss in SciProfiles
first_page
settings
Order Article Reprints
Font Type:
Arial Georgia Verdana
Font Size:
Aa Aa Aa
Line Spacing:
Column Width:
Background:
Article

Optimality for Control Problem with PDEs of Second-Order as Constraints

by
Savin Treanţă
1,*,
Muhammad Bilal Khan
2,* and
Tareq Saeed
3
1
Department of Applied Mathematics, University Politehnica of Bucharest, 060042 Bucharest, Romania
2
Department of Mathematics, COMSATS University Islamabad, Islamabad 44000, Pakistan
3
Nonlinear Analysis and Applied Mathematics—Research Group, Department of Mathematics, Faculty of Sciences, King Abdulaziz University, Jeddah 21589, Saudi Arabia
*
Authors to whom correspondence should be addressed.
Mathematics 2022, 10(6), 977; https://doi.org/10.3390/math10060977
Submission received: 1 March 2022 / Revised: 16 March 2022 / Accepted: 17 March 2022 / Published: 18 March 2022
Versions Notes

Abstract

This paper deals with a class of second-order partial differential equation (in short, PDE) constrained optimal control problems. More specifically, by using appropriate variational techniques, we state necessary conditions of optimality associated with this class of optimization problems, defined by controlled curvilinear integral cost functionals involving partial derivatives of second-order. The importance of the considered problem is provided by its applications in mechanics and physics. Compared with other research works, here we develop a new mathematics context that extends the results obtained so far, both through the use of controlled curvilinear integrals and also by considering partial derivatives of second-order. In addition, to emphasize the usefulness of the main results, an illustrative example is provided.
Keywords: multi-variate controlled Lagrangian of second-order; equations of Euler–Lagrange type; second-order PDE constraints; curvilinear integral multi-variate controlled Lagrangian of second-order; equations of Euler–Lagrange type; second-order PDE constraints; curvilinear integral

Share and Cite

MDPI and ACS Style

Treanţă, S.; Khan, M.B.; Saeed, T. Optimality for Control Problem with PDEs of Second-Order as Constraints. Mathematics 2022, 10, 977. https://doi.org/10.3390/math10060977

AMA Style

Treanţă S, Khan MB, Saeed T. Optimality for Control Problem with PDEs of Second-Order as Constraints. Mathematics. 2022; 10(6):977. https://doi.org/10.3390/math10060977

Chicago/Turabian Style

Treanţă, Savin, Muhammad Bilal Khan, and Tareq Saeed. 2022. "Optimality for Control Problem with PDEs of Second-Order as Constraints" Mathematics 10, no. 6: 977. https://doi.org/10.3390/math10060977

APA Style

Treanţă, S., Khan, M. B., & Saeed, T. (2022). Optimality for Control Problem with PDEs of Second-Order as Constraints. Mathematics, 10(6), 977. https://doi.org/10.3390/math10060977

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

Article Metrics

Back to TopTop