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In this paper we study the conditioning of optimal control problems constrained by linear parabolic equations with Neumann boundary conditions. While we concentrate on a given end-time target function the results hold also when the target…

Numerical Analysis · Mathematics 2025-03-24 Luise Blank

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…

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

Recent strides in nonlinear model predictive control (NMPC) underscore a dependence on numerical advancements to efficiently and accurately solve large-scale problems. Given the substantial number of variables characterizing typical…

Robotics · Computer Science 2024-06-04 Wilson Jallet , Ewen Dantec , Etienne Arlaud , Justin Carpentier , Nicolas Mansard

In this paper, an efficient parallel splitting method is proposed for the optimal control problem with parabolic equation constraints. The linear finite element is used to approximate the state variable and the control variable in spatial…

Optimization and Control · Mathematics 2023-02-21 Haiming Song , Jiachuan Zhang , Yongle Hao

Parallel-in-time algorithms have been successfully employed for reducing time-to-solution of a variety of partial differential equations, especially for diffusive (parabolic-type) equations. A major failing of parallel-in-time approaches to…

Numerical Analysis · Mathematics 2019-08-28 Hans De Sterck , Stephanie Friedhoff , Alexander J. M. Howse , Scott P. MacLachlan

This paper studies a time optimal control problem with control constraints of the rectangular type for the linear multi-input time-varying ordinary differential equations. The aims of this study are to establish certain necessary and…

Optimization and Control · Mathematics 2016-11-25 Can Zhang

An optimal control problem for the continuity equation is considered. The aim of a controller is to maximize the total mass within a target set at a given type moment. An iterative numerical algorithm for solving this problem is presented.

Optimization and Control · Mathematics 2017-08-21 Nikolay Pogodaev

Asynchronous iterations arise naturally in parallel computing if one wants to solve large problems with a minimization of the idle times. This paper presents an original model of asynchronous iterations for a time-domain decomposition…

Distributed, Parallel, and Cluster Computing · Computer Science 2019-07-12 Qinmeng Zou , Guillaume Gbikpi-Benissan , Frederic Magoules

We present a temporal decomposition scheme for solving long-horizon optimal control problems. In the proposed scheme, the time domain is decomposed into a set of subdomains with partially overlapping regions. Subproblems associated with the…

Optimization and Control · Mathematics 2020-04-01 Sungho Shin , Timm Faulwasser , Mario Zanon , Victor M. Zavala

Parareal is a well-studied algorithm for numerically integrating systems of time-dependent differential equations by parallelising the temporal domain. Given approximate initial values at each temporal sub-interval, the algorithm locates a…

Numerical Analysis · Mathematics 2022-07-11 Kamran Pentland , Massimiliano Tamborrino , D. Samaddar , L. C. Appel

The optimal control of two-level systems by time-dependent laser fields is studied using a variational theory. We obtain, for the first time, general analytical expressions for the optimal pulse shapes leading to global maximization or…

Quantum Physics · Physics 2009-11-10 Martin E. Garcia , Ilia Grigorenko

We present variational theory for optimal control over a finite time interval in quantum systems with relaxation. The corresponding Euler-Lagrange equations determining the optimal control field are derived. In our theory the optimal…

Quantum Physics · Physics 2009-11-07 Ilia Grigorenko , Martin E. Garcia , K. H. Bennemann

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

In this work we study the asymptotic behavior of the solutions of a class of abstract parabolic time optimal control problems when the generators converge, in an appropriate sense, to a given strictly negative operator. Our main application…

Optimization and Control · Mathematics 2015-02-09 Marius Tucsnak , Gengsheng Wang , Chi-Ting Wu

A weighted version of the parareal method for parallel-in-time computation of time dependent problems is presented. Linear stability analysis for a scalar weighing strategy shows that the new scheme may enjoy favorable stability properties…

Numerical Analysis · Mathematics 2018-02-09 Gil Ariel , Hieu Nguyen , Richard Tsai

The time domain analysis of eddy current problems often requires the simulation of long time intervals, e.g. until a steady state is reached. Fast-switching excitations e.g. in pulsedwidth modulated signals require in addition very small…

Numerical Analysis · Mathematics 2021-01-05 Idoia Cortes Garcia , Iryna Kulchytska-Ruchka , Markus Clemens , Sebastian Schöps

This paper considers the finite element approximation to parabolic optimal control problems with measure data in a nonconvex polygonal domain. Such problems usually possess low regularity in the state variable due to the presence of measure…

Numerical Analysis · Mathematics 2024-03-12 Pratibha Shakya

This paper introduces Exp-ParaDiag, a novel time-parallel method that combines the strength of exponential integrators into the ParaDiag framework. We develop and analyze Exp-ParaDiag based on first and second order accurate exponential…

Numerical Analysis · Mathematics 2026-03-05 Gobinda Garai , Nagaiah Chamakuri

An optimal control problem for semilinear parabolic partial differential equations is considered. The control variable appears in the leading term of the equation. Necessary conditions for optimal controls are established by the method of…

Optimization and Control · Mathematics 2010-08-20 Hongwei Lou