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In this paper, a local-global model reduction method is presented to solve stochastic optimal control problems governed by partial differential equations (PDEs). If the optimal control problems involve uncertainty, we need to use a few…

Numerical Analysis · Mathematics 2018-07-04 Lingling Ma , Qiuqi Li , Lijian Jiang

This contribution focuses on the development of Model Order Reduction (MOR) for one-way coupled steady state linear thermomechanical problems in a finite element setting. We apply Proper Orthogonal Decomposition (POD) for the computation of…

Model Predictive Control (MPC) is a well-established approach to solve infinite horizon optimal control problems. Since optimization over an infinite time horizon is generally infeasible, MPC determines a suboptimal feedback control by…

Optimization and Control · Mathematics 2022-10-26 Saskia Dietze , Martin A. Grepl

In this paper we study the approximation of a distributed optimal control problem for linear para\-bolic PDEs with model order reduction based on Proper Orthogonal Decomposition (POD-MOR). POD-MOR is a Galerkin approach where the basis…

Optimization and Control · Mathematics 2015-12-08 Alessandro Alla , Carmen Graessle , Michael Hinze

We consider linear model reduction in both the control and state variables for unconstrained linear-quadratic optimal control problems subject to time-varying parabolic PDEs. The first-order optimality condition for a state-space reduced…

Optimization and Control · Mathematics 2025-10-17 Michael Kartmann , Stefan Volkwein

We present a partitioned Model Order Reduction method for multiphysics problems, that is based on a semi-implicit treatment of the coupling conditions, and on a projection scheme. The proposed Reduced Order Method is based on the Proper…

Numerical Analysis · Mathematics 2023-08-08 Monica Nonino , Francesco Ballarin , Gianluigi Rozza , Yvon Maday

Steering a system towards a desired target in a very short amount of time is challenging from a computational standpoint. Indeed, the intrinsically iterative nature of optimal control problems requires multiple simulations of the physical…

Optimization and Control · Mathematics 2025-05-16 Matteo Tomasetto , Andrea Manzoni , Francesco Braghin

A large-scale complex system comprising many, often spatially distributed, dynamical subsystems with partial autonomy and complex interactions are called system of systems. This paper describes an efficient algorithm for model predictive…

Optimization and Control · Mathematics 2019-04-25 Branimir Novoselnik , Vedrana Spudić , Mato Baotić

In this work, we analyze Parametrized Advection-Dominated distributed Optimal Control Problems with random inputs in a Reduced Order Model (ROM) context. All the simulations are initially based on a finite element method (FEM)…

Numerical Analysis · Mathematics 2024-08-27 Fabio Zoccolan , Maria Strazzullo , Gianluigi Rozza

In this work, we aim at efficiently solving a parametrized family of optimal transport problems by using model order reduction methods. We propose a reduced-order model by adding to the primal (respectively dual) version of the…

Numerical Analysis · Mathematics 2026-04-13 Elise Bonnet-Weill , Virginie Ehrlacher , Luca Nenna

We propose a model order reduction technique integrating the Shifted Boundary Method (SBM) with a POD-Galerkin strategy. This approach allows to treat more complex parametrized domains in an efficient and straightforward way. The impact of…

Numerical Analysis · Mathematics 2019-01-11 Efthymios N. Karatzas , Giovanni Stabile , Leo Nouveau , Guglielmo Scovazzi , Gianluigi Rozza

In this paper we will consider distributed Linear-Quadratic Optimal Control Problems dealing with Advection-Diffusion PDEs for high values of the P\'eclet number. In this situation, computational instabilities occur, both for steady and…

Numerical Analysis · Mathematics 2024-05-03 Fabio Zoccolan , Maria Strazzullo , Gianluigi Rozza

We consider model order reduction by proper orthogonal decomposition (POD) for parametrized partial differential equations, where the underlying snapshots are computed with adaptive finite elements. We address computational and theoretical…

Numerical Analysis · Mathematics 2016-09-21 Sebastian Ullmann , Marko Rotkvic , Jens Lang

In this paper, we investigate an optimal control problem governed by parabolic equations with measure-valued controls over time. We establish the well-posedness of the optimal control problem and derive the first-order optimality condition…

Optimization and Control · Mathematics 2024-04-04 Wei Gong , Dongdong Liang

In this work, a novel method with an adaptive functional basis for reduced order models (ROM) based on proper orthogonal decomposition (POD) is introduced. The method is intended to be applied in particular to hydrocarbon reservoir…

Numerical Analysis · Mathematics 2021-06-23 Dmitry Voloskov , Dimitri Pissarenko

We propose a projection-based model order reduction method for the solution of parameter-dependent dynamical systems. The proposed method relies on the construction of time-dependent reduced spaces generated from evaluations of the solution…

Numerical Analysis · Mathematics 2019-09-11 Marie Billaud-Friess , Anthony Nouy

We introduce an alternative approach for the analysis and numerical approximation of the optimal feedback control mapping. It consists in looking at a typical optimal control problem in such a way that feasible controls are mappings…

Optimization and Control · Mathematics 2017-06-09 Pablo Pedregal

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

We investigate an optimization problem governed by an elliptic partial differential equation with uncertain parameters. We introduce a robust optimization framework that accounts for uncertain model parameters. The resulting non-linear…

Optimization and Control · Mathematics 2019-09-24 Alessandro Alla , Michael Hinze , Philip Kolvenbach , Oliver Lass , Stefan Ulbrich

This paper presents a method to approximately solve stochastic optimal control problems in which the cost function and the system dynamics are polynomial. For stochastic systems with polynomial dynamics, the moments of the state can be…

Optimization and Control · Mathematics 2017-02-24 Andrew Lamperski , Khem Raj Ghusinga , Abhyudai Singh