Related papers: Model Reduction For Parametrized Optimal Control P…
Simulating fluid flows in different virtual scenarios is of key importance in engineering applications. However, high-fidelity, full-order models relying, e.g., on the finite element method, are unaffordable whenever fluid flows must be…
In this work, the artificial recirculation of water is presented and analyzed, from the perspective of the optimal control of partial differential equations, as a tool to prevent eutrophication effects in large waterbodies. A novel…
Partial differential equation-based numerical solution frameworks for initial and boundary value problems have attained a high degree of complexity. Applied to a wide range of physics with the ultimate goal of enabling engineering…
In this work a stabilised and reduced Galerkin projection of the incompressible unsteady Navier-Stokes equations for moderate Reynolds number is presented. The full-order model, on which the Galerkin projection is applied, is based on a…
Optimal control problems naturally arise in many scientific applications where one wishes to steer a dynamical system from a certain initial state $\mathbf{x}_0$ to a desired target state $\mathbf{x}^*$ in finite time $T$. Recent advances…
This paper demonstrates a refined approach to solving dynamic optimization problems for underactuated marine surface vessels. To this end the differential flatness of a mathematical model assuming full actuation is exploited to derive an…
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…
This paper presents a model order reduction (MOR) approach for high dimensional problems in the analysis of financial risk. To understand the financial risks and possible outcomes, we have to perform several thousand simulations of the…
A class of time-optimal control problems governed by semilinear parabolic equations with mixed pointwise constraints and final point constraints is considered. By introducing the so-called locally optimal solution to time-optimal control…
This article proposes a new approach based on finite-horizon parameterizing manifolds (PMs) for the design of low-dimensional suboptimal controllers to optimal control problems of nonlinear partial differential equations (PDEs) of parabolic…
We develop a Proper Orthogonal Decomposition (POD)-Galerkin based Reduced Order Model (ROM) for the efficient numerical simulation of the parametric Navier-Stokes equations in the stream function-vorticity formulation. Unlike previous…
This work investigates an elliptic optimal control problem defined on uncertain domains and discretized by a fictitious domain finite element method and cut elements. Key ingredients of the study are to manage cases considering the usually…
In this paper we present a dynamic programing approach to stochastic optimal control problems with dynamic, time-consistent risk constraints. Constrained stochastic optimal control problems, which naturally arise when one has to consider…
Sequential Model-based Bayesian Optimization has been successful-ly applied to several application domains, characterized by complex search spaces, such as Automated Machine Learning and Neural Architecture Search. This paper focuses on…
We present a model predictive control (MPC) framework for linear switched evolution equations arising from a parabolic partial differential equation (PDE). First-order optimality conditions for the resulting finite-horizon optimal control…
Moment optimization techniques have been recently proposed to solve globally various classes of optimal control problems. As those methods return truncated moment sequences of occupation measures, this paper explores a numeric method for…
We propose a data-driven model order reduction (MOR) technique for parametrized partial differential equations that exhibit parameter-dependent jump-discontinuities. Such problems have poor-approximability in a linear space and therefore,…
We consider numerical approaches for deterministic, finite-dimensional optimal control problems whose dynamics depend on unknown or uncertain parameters. We seek to amortize the solution over a set of relevant parameters in an offline stage…
This paper introduces and analyses a continuous optimization approach to solve optimal control problems involving ordinary differential equations (ODEs) and tracking type objectives. Our aim is to determine control or input functions, and…
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…