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In this work, we will investigate the question of optimal control for bilinear systems with constrained endpoint. The optimal control will be characterized through a set of unconstrained minimization problems that approximate the former.…

Optimization and Control · Mathematics 2021-07-28 Soufiane Yahyaoui , Lahoussine Lafhim , Mohamed Ouzahra

In this paper, a quadratic optimal control problem is considered for second-order parabolic PDEs with homogeneous Dirichlet boundary conditions, in which the "point" control function (depending only on time) constitutes a source term. These…

Systems and Control · Electrical Eng. & Systems 2024-07-04 Gilberto O. Corrêa , Marlon M. López-Flores , Alexandre L. Madureira

The paper presents results about strong metric subregularity of the optimality mapping associated with the system of first-order necessary optimality conditions for a problem of optimal control of a semilinear parabolic equation. The…

Optimization and Control · Mathematics 2025-11-19 Alberto Domínguez Corella , Nicolai Jork , Vladimir M. Veliov

This paper deals with optimal control problems for systems affine in the control variable. We consider nonnegativity constraints on the control, and finitely many equality and inequality constraints on the final state. First, we obtain…

Optimization and Control · Mathematics 2013-07-02 Maria Soledad Aronna , J. Frederic Bonnans , Andrei V. Dmitruk , Pablo Lotito

This work concentrates on a class of optimal control problems for semilinear parabolic equations subject to control constraint of the form $\|u(t)\|_{L^1(\Omega)} \le \gamma$ for $t \in (0,T)$. This limits the total control that can be…

Optimization and Control · Mathematics 2021-12-03 Eduardo Casas , Karl Kunisch

Second-order necessary conditions for optimal control problems are considered, where the ``second-order" is in the sense of that Pontryagin's maximum principle is viewed as a first-order necessary optimality condition. A sufficient…

Optimization and Control · Mathematics 2010-08-06 Hongwei Lou

A class of optimal control problems governed by linear fractional diffusion equation with control constraint is considered. We first establish some results on the existence of strong solution to the state equation and the existence of…

Optimization and Control · Mathematics 2022-11-24 Bui Trong Kien , Bui Ngoc Muoi , Ching-Feng Wen , Jen-Chih Yao

We analyze the state constrained inverse Stefan type parabolic free boundary problem as an optimal control problem in the Sobolev-Besov spaces framework. Boundary heat flux, density of heat sources, and free boundary are components of the…

Analysis of PDEs · Mathematics 2017-12-01 Ugur G. Abdulla , Jonathan Goldfarb , Evan Cosgrove , Curtis Earl

In this article we study an optimal control problem subject to the Fokker-Planck equation \[ \partial_t \rho - \nu \Delta \rho - {\rm div } \big(\rho B[u]\big) = 0. \] The control variable $u$ is time-dependent and possibly…

Analysis of PDEs · Mathematics 2021-01-19 M. Soledad Aronna , Fredi Tröltzsch

This paper is dedicated to the analysis of infinite horizon optimal control problems subject to semilinear parabolic equations with constraints on the controls and discounted cost functionals. The discount factors on the cost and the state…

Optimization and Control · Mathematics 2026-04-24 Eduardo Casas , Karl Kunisch

This paper is concerned with the state-constrained optimal control of the three-dimensional thermistor problem, a fully quasilinear coupled system of a parabolic and elliptic PDE with mixed boundary conditions. This system models the…

Optimization and Control · Mathematics 2018-07-02 Hannes Meinlschmidt , Christian Meyer , Joachim Rehberg

We consider a heat conduction problem $S$ with mixed boundary conditions in a n-dimensional domain $\Omega$ with regular boundary $\Gamma$ and a family of problems $S_{\alpha}$, where the parameter $\alpha>0$ is the heat transfer…

Optimization and Control · Mathematics 2019-12-20 Domingo A. Tarzia , Carolina M. Bollo , Claudia M. Gariboldi

This article discusses an optimal control problem for a phase field model of two immiscible incompressible fluid flow, incorporating surface tension effects. The optimal control problem is defined with a $L^2$-cost functional and subject to…

Optimization and Control · Mathematics 2026-05-12 Arghya Kundu

We study local controllability and optimal control problems for invertible discrete-time control systems. We present second order necessary conditions for optimality and sufficient conditions for local controllability. The conditions are…

Optimization and Control · Mathematics 2013-01-30 M. Barbero-Liñán , B. Jakubczyk

In this work, we address some optimal control problems related to the evolution of two isothermal, incompressible, immisible fluids in a two dimensional bounded domain. A distributed optimal control problem is formulated as the minimization…

Optimization and Control · Mathematics 2019-02-19 Tania Biswas , Sheetal Dharmatti , Manil T Mohan

In this manuscript, we consider a control system governed by a general ordinary differential equation on a Riemannian manifold, with its endpoints satisfying some inequalities and equalities, and its control constrained to a closed convex…

Optimization and Control · Mathematics 2020-11-06 Li Deng

Semilinear parabolic systems with bi-linear nonlinearities cover a lot of applications and their optimal control leads to relatively simple optimality conditions. An example is the incompressible Navier-Stokes system for homogeneous fluids,…

Analysis of PDEs · Mathematics 2021-08-31 Tomáš Roubíček

We consider the optimal control of singular nonlinear partial differential equation which is the distributional formulation of the multiphase Stefan type free boundary problem for the general second order parabolic equation. Boundary heat…

Analysis of PDEs · Mathematics 2020-03-03 Ugur G. Abdulla , Evan Cosgrove

In this paper, we are concerned with optimal control problems evolved on Riemannian manifolds, where the initial and final states satisfy some inequality and equality type constraints, and the control set is a separable metric space. We…

Optimization and Control · Mathematics 2020-07-13 Li Deng , Xu Zhang

Infinite horizon open loop optimal control problems for semilinear parabolic equations are investigated. The controls are subject to a cost-functional which promotes sparsity in time. The focus is put on deriving first order optimality…

Optimization and Control · Mathematics 2021-12-14 Eduardo Casas , Karl Kunisch