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

Savin Treanţă, Muhammad Bilal Khan and Tareq Saeed
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Savin Treanţă: Department of Applied Mathematics, University Politehnica of Bucharest, 060042 Bucharest, Romania
Muhammad Bilal Khan: Department of Mathematics, COMSATS University Islamabad, Islamabad 44000, Pakistan
Tareq Saeed: Nonlinear Analysis and Applied Mathematics—Research Group, Department of Mathematics, Faculty of Sciences, King Abdulaziz University, Jeddah 21589, Saudi Arabia

Mathematics, 2022, vol. 10, issue 6, 1-7

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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