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An automated framework is presented for the numerical solution of optimal control problems with PDEs as constraints, in both the stationary and instationary settings. The associated code can solve both linear and non-linear problems, and…

Numerical Analysis · Mathematics 2024-09-02 Santolo Leveque , James R. Maddison , John W. Pearson

In this contribution we develop an efficient reduced order model for solving parametrized linear-quadratic optimal control problems with linear time-varying state system. The fully reduced model combines reduced basis approximations of the…

Numerical Analysis · Mathematics 2024-08-29 Hendrik Kleikamp , Lukas Renelt

We present a new parallel computational framework for the efficient solution of a class of $L^2$/$L^1$-regularized optimal control problems governed by semi-linear elliptic partial differential equations (PDEs). The main difficulty in…

Optimization and Control · Mathematics 2025-08-20 Gabriele Ciaramella , Michael Kartmann , Georg Müller

This paper deals with model-order reduction of parametric partial differential equations (PPDE). More specifically, we consider the problem of finding a good approximation subspace of the solution manifold of the PPDE when only partial…

Numerical Analysis · Mathematics 2017-07-04 C. Herzet , P. Héas , A. Drémeau

A solution to the suboptimal $H^\infty$-control problem is given for a class of hyperbolic partial differential equations (PDEs). The first result of this manuscript shows that the considered class of PDEs admits an equivalent…

Optimization and Control · Mathematics 2025-01-16 Anthony Hastir , Birgit Jacob , Hans Zwart

We present a novel reduced order model (ROM) approach for parameterized time-dependent PDEs based on modern learning. The ROM is suitable for multi-query problems and is nonintrusive. It is divided into two distinct stages: A nonlinear…

Numerical Analysis · Mathematics 2020-11-24 Nikolaj T. Mücke , Sander M. Bohté , Cornelis W. Oosterlee

A common theme in all the above areas is designing a dynamical system to accomplish desired objectives, possibly in some predefined optimal way. Since control theory advances the idea of suitably modifying the behavior of a dynamical…

Optimization and Control · Mathematics 2024-07-03 Revati Gunjal , Syed Shadab Nayyer , Sushama Wagh , Navdeep Singh

In this paper, based on real-time nonlinear receding horizon control methodology, a novel approach is developed for parameter estimation of time invariant and time varying nonlinear dynamical systems in chaotic environments. Here, the…

Optimization and Control · Mathematics 2016-11-21 Fei Sun , Kamran Turkoglu

Solving analytically intractable partial differential equations (PDEs) that involve at least one variable defined on an unbounded domain arises in numerous physical applications. Accurately solving unbounded domain PDEs requires efficient…

Machine Learning · Computer Science 2026-05-12 Mingtao Xia , Lucas Böttcher , Tom Chou

Parametric model order reduction using reduced basis methods can be an effective tool for obtaining quickly solvable reduced order models of parametrized partial differential equation problems. With speedups that can reach several orders of…

Numerical Analysis · Mathematics 2022-01-26 Mario Ohlberger , Stephan Rave

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

This paper presents the design and analysis of a Hybrid High-Order (HHO) approximation for a distributed optimal control problem governed by the Poisson equation. We propose three distinct schemes to address unconstrained control problems…

Numerical Analysis · Mathematics 2025-01-14 Gouranga Mallik , Ramesh Chandra Sau

We consider the design of structure-preserving discretization methods for the solution of systems of boundary controlled Partial Differential Equations (PDEs) thanks to the port-Hamiltonian formalism. We first provide a novel general…

Numerical Analysis · Mathematics 2020-09-30 Andrea Brugnoli , Ghislain Haine , Anass Serhani , Xavier Vasseur

PDE-constrained optimal control problems require regularisation to ensure well-posedness, introducing small perturbations that make the solutions challenging to approximate accurately. We propose a finite element approach that couples both…

Numerical Analysis · Mathematics 2025-03-17 Jenny Power , Tristan Pryer

This paper build on our recent work where we presented a dual stochastic optimal control formulation of the nonlinear filtering problem [1]. The constraint for the dual problem is a backward stochastic differential equations (BSDE). The…

Optimization and Control · Mathematics 2021-11-02 Jin Won Kim , Prashant G. Mehta

Design-space dimensionality reduction is essential to mitigate the cost of high-fidelity simulation-based optimization, especially when dealing with high-dimensional geometric parameterizations. Traditional linear techniques, such as…

Optimization and Control · Mathematics 2025-07-23 Andrea Serani , Giorgio Palma , Jeroen Wackers , Domenico Quagliarella , Stefano Gaggero , Matteo Diez

In this paper, we investigate a decentralized control problem with nested subsystems, which is a general model for one-directional communication amongst many subsystems. The noises in our dynamics are modelled as uncertain variables which…

Optimization and Control · Mathematics 2022-06-14 Aditya Dave , Nishanth Venkatesh , Andreas A. Malikopoulos

In this contribution we apply an adaptive model hierarchy, consisting of a full-order model, a reduced basis reduced order model, and a machine learning surrogate, to parametrized linear-quadratic optimal control problems. The involved…

Optimization and Control · Mathematics 2024-02-19 Hendrik Kleikamp

This paper studies an infinite horizon optimal control problem for discrete-time linear system and quadratic criteria, both with random parameters which are independent and identically distributed with respect to time. In this general…

Optimization and Control · Mathematics 2024-03-04 Deyue Li

We address the stabilization of linear, time-varying parabolic PDEs using finite-dimensional receding horizon controls (RHCs) derived from reduced-order models (ROMs). We first prove exponential stability and suboptimality of the…

Optimization and Control · Mathematics 2026-05-27 Behzad Azmi , Michael Kartmann , Stefan Volkwein