Related papers: Space-time POD-Galerkin approach for parametric fl…
This article contributes to a framework for a computational indirect method based on the Pontryagin maximum principle to efficiently solve a class of state constrained time-optimal control problems in the presence of a time-dependent flow…
Many unsteady flows exhibiting complex dynamics are nevertheless characterized by emergent large-scale coherence in space and time. Reduced-order models based on Galerkin projection of the governing equations onto an orthogonal modal basis…
The objective of this paper is to investigate how noisy and incomplete observations can be integrated in the process of building a reduced-order model. This problematic arises in many scientific domains where there exists a need for…
In order to solve partial differential equations numerically and accurately, a high order spatial discretization is usually needed. Model order reduction (MOR) techniques are often used to reduce the order of spatially-discretized systems…
In this paper, we compare three model order reduction methods: the proper orthogonal decomposition (POD), discrete empirical interpolation method (DEIM) and dynamic mode decomposition (DMD) for the optimal control of the convective…
From the perspective of control theory, the gradient descent optimization methods can be regarded as a dynamic system where various control techniques can be designed to enhance the performance of the optimization method. In this paper, we…
Several nonlinear model reduction techniques are compared for the three cases of the non-parallel version of the Kuramoto-Sivashinsky equation, the transient regime of flow past a cylinder at $Re=100$ and fully developed flow past a…
In feedback flow control, one of the challenges is to develop mathematical models that describe the fluid physics relevant to the task at hand, while neglecting irrelevant details of the flow in order to remain computationally tractable. A…
Time scale separation is a natural property of many control systems that can be ex- ploited, theoretically and numerically. We present a numerical scheme to solve optimal control problems with considerable time scale separation that is…
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…
This paper primarily focuses on the practical applications of optimal control theory for perturbed sweeping processes within the realm of robotics dynamics. By describing these models as controlled sweeping processes with pointwise control…
Plasmas are highly nonlinear and multi-scale, motivating a hierarchy of models to understand and describe their behavior. However, there is a scarcity of plasma models of lower fidelity than magnetohydrodynamics (MHD), although these…
This paper puts forth several closure models for the proper orthogonal decomposition (POD) reduced order modeling of fluid flows. These new closure models, together with other standard closure models, are investigated in the numerical…
An analysis of calibration for reduced-order models (ROMs) is presented in this work. The Galerkin and least-squares Petrov-Galerkin (LSPG) methods are tested on compressible flows involving a disparity of temporal scales. A novel…
This work deals with optimal control problems as a strategy to drive bifurcating solution of nonlinear parametrized partial differential equations towards a desired branch. Indeed, for these governing equations, multiple solution…
We study optimal control of diffusions with slow and fast variables and address a question raised by practitioners: is it possible to first eliminate the fast variables before solving the optimal control problem and then use the optimal…
Reduced order modeling (ROM) provides an efficient framework to compute solutions of parametric problems. Basically, it exploits a set of precomputed high-fidelity solutions --- computed for properly chosen parameters, using a full-order…
By enabling constraint-aware online model adaptation, model predictive control using Gaussian process (GP) regression has exhibited impressive performance in real-world applications and received considerable attention in the learning-based…
We introduce a family of hybrid discretisations for the numerical approximation of optimal control problems governed by the equations of immiscible displacement in porous media. The proposed schemes are based on mixed and discontinuous…
A methodology grounded in model reduction is presented for accelerating the gradient-based solution of a family of linear or nonlinear constrained optimization problems where the constraints include at least one linear Partial Differential…