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Optimal control of the singular nonlinear parabolic PDE which is a distributional formulation of multidimensional and multiphase Stefan-type free boundary problem is analyzed. Approximating sequence of finite-dimensional optimal control…

Analysis of PDEs · Mathematics 2020-06-16 Ugur G. Abdulla , Evan Cosgrove

In this paper, we study optimal control problems of semilinear elliptic and parabolic equations. A tracking cost functional, quadratic in the control and state variables, is considered. No control constraints are imposed. We prove that the…

Optimization and Control · Mathematics 2022-10-21 Eduardo Casas , Daniel Wachsmuth

In this paper, by using the Brunovsky normal form, we provide a reformulation of the problem consisting in finding the actuator design which minimizes the controllability cost for finite-dimensional linear systems with scalar controls. Such…

Optimization and Control · Mathematics 2021-08-13 Borjan Geshkovski , Enrique Zuazua

In this paper we investigate a priori error estimates for the space-time Galerkin finite element discretization of a simplified semilinear gradient enhanced damage model. The model equations are of a special structure as the state equation…

Optimization and Control · Mathematics 2020-04-14 Marita Holtmannspötter , Arnd Rösch

We develop a new variational formulation of the inverse Stefan problem, where information on the heat flux on the fixed boundary is missing and must be found along with the temperature and free boundary. We employ optimal control framework,…

Analysis of PDEs · Mathematics 2015-06-09 Ugur G. Abdulla

Many physical phenomena, governed by partial differential equations (PDEs), are second order in nature. This makes sense to pose the control on the second order derivatives of the field solution, in addition to zero and first order ones, to…

Optimization and Control · Mathematics 2010-10-11 Rouhollah Tavakoli

PDE-constrained optimal control problems require regularisation to ensure well-posedness, introducing small perturbations that make the solutions challenging to approximate accurately. We propose a finite element approach that couples both…

Numerical Analysis · Mathematics 2025-03-17 Jenny Power , Tristan Pryer

We study high-dimensional stochastic optimal control problems in which many agents cooperate to minimize a convex cost functional. We consider both the full-information problem, in which each agent observes the states of all other agents,…

Probability · Mathematics 2023-01-10 Joe Jackson , Daniel Lacker

We present a branch-and-bound algorithm for globally solving parabolic optimal control problems with binary switches that have bounded variation and possibly need to satisfy further combinatorial constraints. More precisely, for a given…

Optimization and Control · Mathematics 2024-01-19 Christoph Buchheim , Alexandra Grütering , Christian Meyer

We study an optimal control problem for the stochastic wave equation driven by affine multiplicative noise, formulated as a stochastic linear-quadratic (SLQ) problem. By applying a stochastic Pontryagin's maximum principle, we characterize…

Optimization and Control · Mathematics 2025-10-30 Abhishek Chaudhary

H-infinity optimal control and estimation are addressed for a class of systems governed by partial differential equations with bounded input and output operators. Diffusion equations are an important example in this class. Explicit formulas…

Optimization and Control · Mathematics 2021-06-09 Carolina Bergeling , Kirsten A. Morris , Anders Rantzer

We consider the finite element discretization of an optimal Dirichlet boundary control problem for the Laplacian, where the control is considered in $H^{1/2}(\Gamma)$. To avoid computing the latter norm numerically, we realize it using the…

Numerical Analysis · Mathematics 2018-11-26 Michael Karkulik

This work is devoted to the reconstruction of the initial temperature in the backward heat equation using the space-time finite element method on fully unstructured space-time simplicial meshes proposed by Steinbach (2015). Such a severely…

Numerical Analysis · Mathematics 2021-04-01 Ulrich Langer , Olaf Steinbach , Fredi Tröltzsch , Huidong Yang

This paper focuses on the optimal control of a class of stochastic Volterra integral equations. Here the coefficients are regular and not assumed to be of convolution type. We show that, under mild regularity assumptions, these equations…

Probability · Mathematics 2026-04-08 Dylan Possamaï , Mehdi Talbi

Autonomous systems have witnessed a rapid increase in their capabilities, but it remains a challenge for them to perform tasks both effectively and safely. The fact that performance and safety can sometimes be competing objectives renders…

Systems and Control · Electrical Eng. & Systems 2024-12-04 Hao Wang , Adityaya Dhande , Somil Bansal

We construct and analyze a multiscale finite element method for an elliptic distributed optimal control problem with pointwise control constraints, where the state equation has rough coefficients. We show that the performance of the…

Numerical Analysis · Mathematics 2023-09-29 Susanne C. Brenner , Jose C. Garay , Li-yeng Sung

The present study investigates a linear-quadratic Dirichlet control problem governed by a non-coercive elliptic equation posed on a possibly non-convex polygonal domain. Tikhonov regularization is carried out in an energy seminorm. The…

Optimization and Control · Mathematics 2026-03-11 Thomas Apel , Mariano Mateos , Arnd Rösch

In this paper, we investigate optimal control problems governed by semilinear elliptic variational inequalities involving constraints on the state, and more precisely the obstacle problem. Since we adopt a numerical point of view, we first…

Optimization and Control · Mathematics 2020-07-10 El Hassene Osmani , Mounir Haddou , Naceurdine Bensalem

This paper studies the problem of steering a linear time-invariant system subject to state and input constraints towards a goal location that may be inferred only through partial observations. We assume mixed-observable settings, where the…

Optimization and Control · Mathematics 2022-11-22 Ugo Rosolia , Yuxiao Chen , Shreyansh Daftry , Masahiro Ono , Yisong Yue , Aaron D. Ames

The purpose of this paper is to establish first and second order necessary optimality conditions for optimal control problems of stochastic evolution equations with control and state constraints. The control acts both in the drift and…

Optimization and Control · Mathematics 2019-01-23 Hélène Frankowska , Qi Lü