English
Related papers

Related papers: Reduction for constrained variational problems on …

200 papers

- We discuss the approximation of distributed null controls for partial differential equations. The main purpose is to determine an approximation of controls that drives the solution from a prescribed initial state at the initial time to…

Optimization and Control · Mathematics 2015-10-14 Arnaud Münch , Pablo Pedregal

A geometric derivation of numerical integrators for optimal control problems is proposed. It is based in the classical technique of generating functions adapted to the special features of optimal control problems.

Optimization and Control · Mathematics 2025-10-20 M. de Leon , D. Martin de Diego , A. Santamaria-Merino

Retractions maps are used to define a discretization of the tangent bundle of the configuration manifold as two copies of the configuration manifold where the dynamics take place. Such discretization maps can be conveniently lifted to the…

Optimization and Control · Mathematics 2022-03-03 María Barbero Liñán , David Martín de Diego

We derive novel algorithms for optimization problems constrained by partial differential equations describing multiscale particle dynamics, including non-local integral terms representing interactions between particles. In particular, we…

Numerical Analysis · Mathematics 2021-09-09 Mildred Aduamoah , Benjamin D. Goddard , John W. Pearson , Jonna C. Roden

This paper discusses the energy optimal control problem for the class of quantum systems that possess dynamical symmetry of SU(1,1), which are widely studied in various physical problems in the quantum theory. Based on the maximum principle…

Optimization and Control · Mathematics 2007-09-13 Jian-Wu Wu , Chun-Wen Li , Jing Zhang , Tzyh-Jong Tarn

We introduce an approximation method to solve an optimal control problem via the Lagrange dual of its weak formulation. It is based on a sum-of-squares representation of the Hamiltonian, and extends a previous method from polynomial…

Optimization and Control · Mathematics 2021-10-15 Eloïse Berthier , Justin Carpentier , Alessandro Rudi , Francis Bach

We provide a framework for the numerical approximation of distributed optimal control problems, based on least-squares finite element methods. Our proposed method simultaneously solves the state and adjoint equations and is $\inf$--$\sup$…

Numerical Analysis · Mathematics 2023-08-03 Thomas Führer , Michael Karkulik

This work is concerned with the time optimal control problem for evolution equations in Hilbert spaces. The attention is focused on the maximum principle for the time optimal controllers having the dimension smaller that of the state…

Analysis of PDEs · Mathematics 2020-04-22 Gabriela Marinoschi

Infinite-dimensional linear conic formulations are described for nonlinear optimal control problems. The primal linear problem consists of finding occupation measures supported on optimal relaxed controlled trajectories, whereas the dual…

Optimization and Control · Mathematics 2014-07-08 Didier Henrion , Edouard Pauwels

In this article we show the crucial role of elliptic regularity theory for the development of efficient numerical methods for the solution of some variational problems. Here we focus to a class of elliptic multiobjective optimal control…

Optimization and Control · Mathematics 2021-01-27 A. Dreves , J. Gwinner , N. Ovcharova

We address the generalized variational problem of Herglotz from an optimal control point of view. Using the theory of optimal control, we derive a generalized Euler-Lagrange equation, a transversality condition, a DuBois-Reymond necessary…

Optimization and Control · Mathematics 2015-06-22 Simao P. S. Santos , Natalia Martins , Delfim F. M. Torres

The linear programming (LP) approach is, together with value iteration and policy iteration, one of the three fundamental methods to solve optimal control problems in a dynamic programming setting. Despite its simple formulation,…

Systems and Control · Electrical Eng. & Systems 2023-10-31 Lucia Falconi , Andrea Martinelli , John Lygeros

In recent years, much effort in designing numerical methods for the simulation and optimization of mechanical systems has been put into schemes which are structure preserving. One particular class are variational integrators which are…

Optimization and Control · Mathematics 2015-05-08 Cédric M. Campos , Sina Ober-Blöbaum , Emmanuel Trélat

This paper is concerned with the state-constrained optimal control of the three-dimensional thermistor problem, a fully quasilinear coupled system of a parabolic and elliptic PDE with mixed boundary conditions. This system models the…

Optimization and Control · Mathematics 2018-07-02 Hannes Meinlschmidt , Christian Meyer , Joachim Rehberg

A finite horizon linear quadratic(LQ) optimal control problem is studied for a class of discrete-time linear fractional systems (LFSs) affected by multiplicative, independent random perturbations. Based on the dynamic programming technique,…

Optimization and Control · Mathematics 2016-07-01 J. J. Trujillo , V. M. Ungureanu

This paper continues the investigations from [7] and is concerned with the derivation of first-order conditions for a control constrained optimization problem governed by a non-smooth elliptic PDE. The control enters the state equation not…

Optimization and Control · Mathematics 2025-02-11 Livia Betz

We consider a linear-quadratic pde constrained optimal control problem on an evolving surface with pointwise state constraints. We reformulate the optimization problem on a fixed surface and approximate the reformulated problem by a…

Optimization and Control · Mathematics 2016-04-27 Michael Hinze , Heiko Kröner

We consider a series of optimal control problems with 2-dimensional control lying in an arbitrary convex compact set $\Omega$. The considered problems are well studied for the case when $\Omega$ is a unit disc, but barely studied for…

Optimization and Control · Mathematics 2021-04-13 A. A. Ardentov , L. V. Lokutsievskiy , Yu. L. Sachkov

This paper investigates numerical methods for solving stochastic linear quadratic (SLQ) optimal control problems governed by stochastic partial differential equations (SPDEs). Two distinct approaches, the open-loop and closed-loop ones, are…

Optimization and Control · Mathematics 2024-11-19 Andreas Prohl , Yanqing Wang

This article concerns a class of time-optimal state constrained control problems with dynamics defined by an ordinary differential equation involving a three-dimensional steady flow vector field. The problem is solved via an indirect method…

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