English
Related papers

Related papers: Error estimates for space-time discretization of p…

200 papers

This paper aims at solving an optimal control problem governed by an anisotropic Allen-Cahn equation numerically. Therefore we first prove the Fr\'echet differentiability of an in time discretized parabolic control problem under certain…

Optimization and Control · Mathematics 2024-08-12 Luise Blank , Johannes Meisinger

In this paper, we derive a bang-bang property of a kind of time optimal control problem for some semilinear heat equation on bounded $C^2$ domains (of the Euclidean space), with homogeneous Dirichlet boundary condition and controls…

Optimization and Control · Mathematics 2015-10-14 Lijuan Wang , Qishu Yan

We consider a general linear parabolic problem with extended time boundary conditions (including initial value problems and periodic ones), and approximate it by the implicit Euler scheme in time and the Gradient Discretisation method in…

Numerical Analysis · Mathematics 2023-08-22 J Droniou , R Eymard , T Gallouët , C Guichard , R Herbin

The paper aims at the development of an apparatus for analysis and construction of near optimal solutions of singularly perturbed (SP) optimal controls problems (that is, problems of optimal control of SP systems) considered on the infinite…

Optimization and Control · Mathematics 2014-08-20 Vladimir Gaitsgory , Sergei Rossomakhine

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

A computational method for the synthesis of time-optimal feedback control laws for linear nilpotent systems is proposed. The method is based on the use of the bang-bang theorem, which leads to a characterization of the time-optimal…

Optimization and Control · Mathematics 2026-05-20 Sara Bicego , Samuel Gue , Dante Kalise , Nelly Villamizar

The paper deals with an optimal control problem in a dynamical system described by a linear differential equation with the Caputo fractional derivative. The goal of control is to minimize a Bolza-type cost functional, which consists of two…

Optimization and Control · Mathematics 2019-09-25 Mikhail Gomoyunov

This work presents the multiharmonic analysis and derivation of functional type a posteriori estimates of a distributed eddy current optimal control problem and its state equation in a time-periodic setting. The existence and uniqueness of…

Optimization and Control · Mathematics 2023-08-10 Monika Wolfmayr

In this paper, we study some control problems that derive from time optimal control of coupled spin dynamics in NMR spectroscopy and quantum information and computation. Time optimal control helps to minimize relaxation losses. The ability…

Quantum Physics · Physics 2017-09-05 Navin Khaneja

In this paper, we study the optimal control problem for steering the state covariance of a discrete-time linear stochastic system over a finite time horizon. First, we establish the existence and uniqueness of the optimal control law for a…

Systems and Control · Electrical Eng. & Systems 2024-10-08 Fengjiao Liu , George Rapakoulias , Panagiotis Tsiotras

We study the stochastic $p$-Laplace system in a bounded domain. We propose two new space-time discretizations based on the approximation of time-averaged values. We establish linear convergence in space and $1/2$ convergence in time.…

Numerical Analysis · Mathematics 2023-05-19 Lars Diening , Martina Hofmanová , Jörn Wichmann

We consider optimal control problems involving two constraint sets: one comprised of linear ordinary differential equations with the initial and terminal states specified and the other defined by the control variables constrained by simple…

Optimization and Control · Mathematics 2024-01-17 Regina S. Burachik , C. Yalçın Kaya , Walaa M. Moursi

This paper presents a new observability estimate for parabolic equations in $\Omega\times(0,T)$, where $\Omega$ is a convex domain. The observation region is restricted over a product set of an open nonempty subset of $\Omega$ and a subset…

Analysis of PDEs · Mathematics 2011-09-20 Kim Dang Phung , Gengsheng Wang

This paper provides necessary conditions of optimality for optimal control problems with time delays in both state and control variables. Different versions of the necessary conditions cover fixed end-time problems and, under additional…

Dynamical Systems · Mathematics 2017-01-09 Andrea Boccia , Richard B. Vinter

We consider a class of stochastic optimal control problems with partial observation, and study their approximation by discrete-time control problems. We establish a convergence result by using weak convergence technique of Kushner and…

Optimization and Control · Mathematics 2023-05-22 Yunzhang Li , Xiaolu Tan , Shanjian Tang

In this paper, we discuss our recent works on the null-controllability, the exact controllability, and the stabilization of linear hyperbolic systems in one dimensional space using boundary controls on one side for the optimal time. Under…

Optimization and Control · Mathematics 2020-12-11 Jean-Michel Coron , Hoai-Minh Nguyen

We propose a time-implicit, finite-element based space-time discretization of the necessary and sufficient optimality conditions for the stochastic linear-quadratic optimal control problem with the stochastic heat equation driven by linear…

Optimization and Control · Mathematics 2020-12-09 Andreas Prohl , Yanqing Wang

An optimal control problem for the linear wave equation with control cost chosen as the BV semi-norm in time is analyzed. This formulation enhances piecewise constant optimal controls and penalizes the number of jumps. Existence of optimal…

Optimization and Control · Mathematics 2018-09-11 Sebastian Engel , Karl Kunisch

In this paper, we study two subjects on internally controlled heat equations with time varying potentials: the attainable subspaces and the bang-bang property for some time optimal control problems. We present some equivalent…

Optimization and Control · Mathematics 2014-04-22 Gengsheng Wang , Yashan Xu , Yubiao Zhang

We consider optimal control problems for partial differential equations where the controls take binary values but vary over the time horizon, they can thus be seen as dynamic switches. The switching patterns may be subject to combinatorial…

Optimization and Control · Mathematics 2024-04-04 Christoph Buchheim , Alexandra Grütering , Christian Meyer