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This paper deals with the optimal stopping problem under partial observation for piecewise-deterministic Markov processes. We first obtain a recursive formulation of the optimal filter process and derive the dynamic programming equation of…

Probability · Mathematics 2013-05-28 Adrien Brandejsky , Benoîte de Saporta , François Dufour

In this work, we use the integral definition of the fractional Laplace operator and study a sparse optimal control problem involving a fractional, semilinear, and elliptic partial differential equation as state equation; control constraints…

Optimization and Control · Mathematics 2023-12-14 Francisco Bersetche , Francisco Fuica , Enrique Otarola , Daniel Quero

In this paper we introduce a new notion of optimal control, or source identification in inverse, problems with fractional parabolic PDEs as constraints. This new notion allows a source/control placement outside the domain where the PDE is…

Optimization and Control · Mathematics 2019-04-16 Harbir Antil , Deepanshu Verma , Mahamadi Warma

This paper studies an optimal control problem for continuous-time stochastic systems subject to reachability objectives specified in a subclass of metric interval temporal logic specifications, a temporal logic with real-time constraints.…

Systems and Control · Computer Science 2015-04-21 Jie Fu , Ufuk Topcu

In this note, we consider the existence and uniqueness of the solution of a time-dependent optimal control problem constrained by a partial differential equation with uncertain inputs. Relying on the Lions' Lemma for deterministic problems,…

Optimization and Control · Mathematics 2018-10-04 Peter Benner , Akwum Onwunta , Martin Stoll

The Pontryagin's Maximum Principle allows, in most cases, the design of optimal controls of affine nonlinear control systems by considering the sign of a smooth function. There are cases, although, where this function vanishes on a whole…

Optimization and Control · Mathematics 2013-11-12 Eduardo Oda , Pedro Aladar Tonelli

The paper addresses an optimal control problem for a perturbed sweeping process of the rate-independent hysteresis type described by a controlled "play and stop" operator with separately controlled perturbations. This problem can be reduced…

Optimization and Control · Mathematics 2015-12-01 Tan H. Cao , Boris S. Mordukhovich

We consider a semilinear parabolic equation with a large class of nonlinearities without any growth conditions. We discretize the problem with a discontinuous Galerkin scheme dG(0) in time (which is a variant of the implicit Euler scheme)…

Numerical Analysis · Mathematics 2018-08-17 Dominik Meidner , Boris Vexler

In this paper we study the approximation of a distributed optimal control problem for linear para\-bolic PDEs with model order reduction based on Proper Orthogonal Decomposition (POD-MOR). POD-MOR is a Galerkin approach where the basis…

Optimization and Control · Mathematics 2015-12-08 Alessandro Alla , Carmen Graessle , Michael Hinze

This paper is concerned with the analysis of a class of optimal control problems governed by a time-harmonic eddy current system with a dipole source, which is taken as the control variable. A mathematical model is set up for the state…

Optimization and Control · Mathematics 2019-12-04 Gabriele Caselli

We construct a space-time parallel method for solving parabolic partial differential equations by coupling the Parareal algorithm in time with overlapping domain decomposition in space. The goal is to obtain a discretization consisting of…

Numerical Analysis · Mathematics 2022-01-17 Jehanzeb Chaudhry , Donald Estep , Simon Tavener

We consider a linear parabolic problem with random elliptic operator in the usual Gelfand triple setting. We do not assume uniform bounds on the coercivity and boundedness constants, but allow them to be random variables. The parabolic…

Analysis of PDEs · Mathematics 2016-04-26 Stig Larsson , Christian Mollet , Matteo Molteni

In this contribution we propose reduced order methods to fast and reliably solve parametrized optimal control problems governed by time dependent nonlinear partial differential equations. Our goal is to provide a tool to deal with the time…

Numerical Analysis · Mathematics 2023-08-08 Francesco Ballarin , Gianluigi Rozza , Maria Strazzullo

Convergence results are shown for full discretizations of quasilinear parabolic partial differential equations on evolving surfaces. As a semidiscretization in space the evolving surface finite element method is considered, using a…

Numerical Analysis · Mathematics 2015-04-01 Balázs Kovács , Christian Andreas Power Guerra

The aim of this work is the numerical homogenization of a parabolic problem with several time and spatial scales using the heterogeneous multiscale method. We replace the actual cell problem with an alternate one, using Dirichlet boundary…

Numerical Analysis · Mathematics 2022-10-11 Daniel Eckhardt , Barbara Verfürth

An adaptive direct collocation method is developed for solving optimal control problems constrained by parabolic partial differential equations. The partial differential equation is first reformulated in a variational setting, where the…

Optimization and Control · Mathematics 2026-03-18 Alexander M. Davies , Sara Pollock , Miriam E. Dennis , Anil V. Rao

The present work addresses a finite-horizon linear-quadratic optimal control problem for uncertain systems driven by piecewise constant controls. The precise values of the system parameters are unknown, but assumed to belong to a finite set…

Systems and Control · Computer Science 2021-08-05 Félix A. Miranda , Fernando Castaños , Alexander Poznyak

We analyze an optimal control problem with pointwise tracking for a fractional semilinear elliptic partial differential equation. The diffusion is characterized by the spectral fractional Laplacian $(-\Delta)^s$ with $s \in (1/2,1)$, a…

Optimization and Control · Mathematics 2026-04-17 Enrique Otarola , Abner J. Salgado

The maximal regularity property of discontinuous Galerkin methods for linear parabolic equations is used together with variational techniques to establish a priori and a posteriori error estimates of optimal order under optimal regularity…

Numerical Analysis · Mathematics 2024-12-13 Georgios Akrivis , Stig Larsson

We propose and analyze a posteriori error estimates for a control-constrained optimal control problem with bang-bang solutions. We consider a solution strategy based on the variational approach, where the control variable is not…

Optimization and Control · Mathematics 2025-05-26 Francisco Fuica