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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

The article examines a linear-quadratic Neumann control problem that is governed by a non-coercive elliptic equation. Due to the non-self-adjoint nature of the linear control-to-state operator, it is necessary to independently study both…

Optimization and Control · Mathematics 2025-06-25 Thomas Apel , Mariano Mateos , Arnd Rösch

We consider the decidability of state-to-state reachability in linear time-invariant control systems over continuous time. We analyse this problem with respect to the allowable control sets, which are assumed to be the image under a linear…

Optimization and Control · Mathematics 2021-03-16 Mohan Dantam , Amaury Pouly

We establish a variety of results extending the well-known Pontryagin maximum principle of optimal control to discrete-time optimal control problems posed on smooth manifolds. These results are organized around a new theorem on critical and…

Optimization and Control · Mathematics 2017-07-14 Robert Kipka , Rohit Gupta

This work discusses the finite element discretization of an optimal control problem for the linear wave equation with time-dependent controls of bounded variation. The main focus lies on the convergence analysis of the discretization…

Optimization and Control · Mathematics 2019-07-26 Sebastian Engel , Philip Trautmann , Boris Vexler

An optimal control problem on finite-dimensional positive cones is stated. Under a critical assumption on the cone, the corresponding Bellman equation is satisfied by a linear function, which can be computed by convex optimization. A…

Optimization and Control · Mathematics 2024-10-02 Richard Pates , Anders Rantzer

We present a finite element method along with its analysis for the optimal control of a model free boundary problem with surface tension effects, formulated and studied in \cite{HAntil_RHNochetto_PSodre_2014a}. The state system couples the…

Optimization and Control · Mathematics 2015-01-05 Harbir Antil , Ricardo H. Nochetto , Patrick Sodré

This article concerns the problem of computing solutions to state-constrained optimal control problems whose trajectory is affected by a flow field. This general mathematical framework is particularly pertinent to the requirements…

Optimization and Control · Mathematics 2022-06-30 Roman Chertovskih , Nathalie T. Khalil , Dmitry Karamzin , Fernando Lobo Pereira

Existing methods for nonlinear robust control often use scenario-based approaches to formulate the control problem as nonlinear optimization problems. Increasing the number of scenarios improves robustness, while increasing the size of the…

Optimization and Control · Mathematics 2023-06-09 Marta Zagorowska , Paola Falugi , Edward O'Dwyer , Eric C. Kerrigan

Nonlinear optimization-based control policies, such as those those arising in nonlinear Model Predictive Control, have seen remarkable success in recent years. These policies require solving computationally demanding nonlinear optimization…

Optimization and Control · Mathematics 2025-12-02 Riccardo Zuliani , Efe C. Balta , John Lygeros

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

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 present a constructive method to devise boundary conditions for solutions of second-order elliptic equations so that these solutions satisfy specific qualitative properties such as: (i) the norm of the gradient of one solution is bounded…

Analysis of PDEs · Mathematics 2012-10-16 Guillaume Bal , Matias Courdurier

In this paper we consider a parabolic optimal control problem with a Dirac type control with moving point source in two space dimensions. We discretize the problem with piecewise constant functions in time and continuous piecewise linear…

Numerical Analysis · Mathematics 2018-08-17 Dmitriy Leykekhman , Boris Vexler

In the contest of optimal control problems, regularity results for optima are known when addressing fiber-strictly convex Lagrangian. For infinite time horizons, or for settings with infinite dimensional dynamics, the equivalence between…

Optimization and Control · Mathematics 2022-12-06 Vincenzo Basco

In this paper, we investigate optimal control problems for Allen-Cahn equations with singular nonlinearities and a dynamic boundary condition involving singular nonlinearities and the Laplace-Beltrami operator. The approach covers both the…

Analysis of PDEs · Mathematics 2014-10-27 Pierluigi Colli , Jürgen Sprekels

A re-entrant manufacturing system producing a large number of items and involving many steps can be approximately modeled by a hyperbolic partial differential equation (PDE) according to mass conservation law with respect to a continuous…

Optimization and Control · Mathematics 2016-11-15 Xiaodong Xu , Stevan Dubljevic

The linear quadratic regulator problem is central in optimal control and was investigated since the very beginning of control theory. Nevertheless, when it includes affine state constraints, it remains very challenging from the classical…

Optimization and Control · Mathematics 2021-03-30 Pierre-Cyril Aubin-Frankowski

In this paper, the optimal strong error estimates for stochastic parabolic optimal control problem with additive noise and integral state constraint are derived based on time-implicit and finite element discretization. The continuous and…

Optimization and Control · Mathematics 2025-05-13 Qiming Wang , Wanfang Shen , Wenbin Liu

Existing methods for nonlinear robust control often use scenario-based approaches to formulate the control problem as large nonlinear optimization problems. The optimization problems are challenging to solve due to their size, especially if…

Optimization and Control · Mathematics 2023-10-19 Marta Zagorowska , Paola Falugi , Edward O'Dwyer , Eric C. Kerrigan