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In this work, we consider optimal control problems for mechanical systems on vector spaces with fixed initial and free final state and a quadratic Lagrange term. Specifically, the dynamics is described by a second order ODE containing an…

We adopt the integral definition of the fractional Laplace operator and study an optimal control problem on Lipschitz domains that involves a fractional elliptic partial differential equation (PDE) as state equation and a control variable…

Numerical Analysis · Mathematics 2024-02-14 Francisco Bersetche , Francisco Fuica , Enrique Otarola , Daniel Quero

This paper proposes an optimal control problem for a parabolic equation with a nonlocal nonlinearity. The system is described by a parabolic equation involving a nonlinear term that depends on the solution and its integral over the domain.…

Optimization and Control · Mathematics 2024-03-20 Cyrille Kenne , Landry Djomegne , Gisèle Mophou

In this paper we study the optimal control of a parabolic initial-boundary value problem of Allen--Cahn type with dynamic boundary conditions. Phase field systems of this type govern the evolution of coupled diffuse phase transition…

Optimization and Control · Mathematics 2023-03-30 Jürgen Sprekels , Fredi Tröltzsch

In this work we study an optimal control problem subject to the instationary Navier-Stokes equations, where the control enters via an inhomogeneous Neumann/Do-Nothing boundary condition. Despite the Navier-Stokes equations with these…

Optimization and Control · Mathematics 2026-05-20 Boris Vexler , Jakob Wagner

In this paper, we focus on a method based on optimal control to address the optimization problem. The objective is to find the optimal solution that minimizes the objective function. We transform the optimization problem into optimal…

Optimization and Control · Mathematics 2023-09-12 Yeming Xu , Ziyuan Guo , Hongxia Wang , Huanshui Zhang

In this paper, we study an optimal boundary control problem for a model for phase separation taking place in a spatial domain that was introduced by P. Podio-Guidugli in Ric. Mat. 55 (2006), pp. 105-118. The model consists of a strongly…

Analysis of PDEs · Mathematics 2017-09-01 Pierluigi Colli , Jürgen Sprekels

An optimal control problem driven by an ordinary differential equation under continuous state constraints is considered in this study. From an operational point of view, we introduce a discrete state constraints optimal control problem and…

Optimization and Control · Mathematics 2018-12-04 Shuzhen Yang

This paper concerns the theoretical and numerical analysis of a free boundary problem for the Laplace equation, with a curvature condition on the free boundary. This boundary is described as the graph of a function, and contact angles are…

Numerical Analysis · Mathematics 2017-07-04 Ivan Fumagalli

We consider a stochastic control problem where the set of controls is not necessarily convex and the system is governed by a nonlinear backward stochastic differential equation. We establish necessary as well as sufficient conditions of…

Probability · Mathematics 2008-12-20 Seid Bahlali

In this article we study optimal control problems for systems that are affine with respect to some of the control variables and nonlinear in relation to the others. We consider finitely many equality and inequality constraints on the…

Optimization and Control · Mathematics 2019-01-15 M. Soledad Aronna

This note is concerned with an optimal control problem governed by the relativistic Maxwell-Newton-Lorentz equations, which describes the motion of charges particles in electro-magnetic fields and consists of a hyperbolic PDE system coupled…

Optimization and Control · Mathematics 2014-11-27 C. Meyer , S. M. Schnepp , O. Thoma

We consider an optimal control problem in which the state is governed by an unilateral obstacle problem (with obstacle from below) and restricted by a pointwise state constraint (from above). In the presence of control constraints, we…

Optimization and Control · Mathematics 2021-01-01 Ira Neitzel , Gerd Wachsmuth

The well-posedness of a class of optimal control problems is analysed, where the state equation couples a nonlinear degenerate Fokker-Planck equation with a system of Ordinary Differential Equations (ODEs). Such problems naturally arise as…

Optimization and Control · Mathematics 2024-11-01 Francesca Anceschi , Giacomo Ascione , Daniele Castorina , Francesco Solombrino

In this paper, a sub-optimal boundary control strategy for a free boundary problem is investigated. The model is described by a non-smooth convection-diffusion equation. The control problem is addressed by an instantaneous strategy based on…

Optimization and Control · Mathematics 2020-11-06 Youness Mezzan , Moulay Hicham Tber

We introduce an alternative approach for the analysis and numerical approximation of the optimal feedback control mapping. It consists in looking at a typical optimal control problem in such a way that feasible controls are mappings…

Optimization and Control · Mathematics 2017-06-09 Pablo Pedregal

In this paper we establish second-order sufficient optimality conditions for a boundary control problem that has been introduced and studied by three of the authors in the preprint arXiv:1407.3916. This control problem regards the viscous…

Analysis of PDEs · Mathematics 2014-11-18 Pierluigi Colli , M. Hassan Farshbaf-Shaker , Gianni Gilardi , Jürgen Sprekels

We study the behavior of $p$-Dirichlet optimal design problem with volume constraint for $p$ large. As the limit as $p$ goes to infinity, we find a limiting free boundary problem governed by the infinity-Laplacian operator. We establish a…

Analysis of PDEs · Mathematics 2009-04-02 J. D. Rossi , E. V. Teixeira

We propose a fine analysis of second order optimality conditions for the optimal control of semi-linear parabolic equations with respect to the initial condition. More precisely, we investigate the following problem: maximise with respect…

Optimization and Control · Mathematics 2022-10-07 Idriss Mazari-Fouquer , Grégoire Nadin

We consider an optimal control problem constrained by a parabolic partial differential equation (PDE) with Robin boundary conditions. We use a well-posed space-time variational formulation in Lebesgue--Bochner spaces with minimal…

Numerical Analysis · Mathematics 2022-12-06 Nina Beranek , M. Alexander Reinhold , Karsten Urban