Related papers: An adaptive POD approximation method for the contr…
We present a novel artificial diffusion method to circumvent the instabilities associated with the standard finite element approximation of convection-diffusion equations. Motivated by the micromorphic approach, we introduce an auxiliary…
For an infinite-horizon control problem, the optimal control can be represented by the stable manifold of the characteristic Hamiltonian system of Hamilton-Jacobi-Bellman (HJB) equation in a semiglobal domain. In this paper, we first…
Optimal control problems are inherently hard to solve as the optimization must be performed simultaneously with updating the underlying system. Starting from an initial guess, Howard's policy improvement algorithm separates the step of…
We propose a finite-dimensional control-based method to approximate solution operators for evolutional partial differential equations (PDEs), particularly in high-dimensions. By employing a general reduced-order model, such as a deep neural…
We derive a posteriori error estimators for an optimal control problem governed by a convection-reaction-diffusion equation; control constraints are also considered. We consider a family of low-order stabilized finite element methods to…
Optimal control problems driven by evolutionary partial differential equations arise in many industrial applications and their numerical solution is known to be a challenging problem. One approach to obtain an optimal feedback control is…
We present a numerical algorithm that allows the approximation of optimal controls for stochastic reaction-diffusion equations with additive noise by first reducing the problem to controls of feedback form and then approximating the…
In this work, a numerical simulation of 1D Burgers' equation is developed using finite difference method and a reduced order model (ROM) of the simulation is developed using proper orthogonal decomposition (POD). The objective of this work…
In this work we propose tailored model order reduction for varying boundary optimal control problems governed by parametric partial differential equations. With varying boundary control, we mean that a specific parameter changes where the…
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…
The error analysis of a proper orthogonal decomposition (POD) data assimilation (DA) scheme for the Navier-Stokes equations is carried out. A grad-div stabilization term is added to the formulation of the POD method. Error bounds with…
In this paper, we present the periodic modifier-adaptation formulation of the dynamic real time optimization. The proposed formulation uses gradient information to update the problem with affine modifiers so that, upon convergence, its…
In this paper we propose and analyze a method based on the Riccati transformation for solving the evolutionary Hamilton-Jacobi-Bellman equation arising from the stochastic dynamic optimal allocation problem. We show how the fully nonlinear…
We consider the approximation of some optimal control problems for the Navier-Stokes equation via a Dynamic Programming approach. These control problems arise in many industrial applications and are very challenging from the numerical point…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
We present an exact mathematical transformation which converts a wide class of advection-diffusion equations into a form allowing simple and direct spatial discretization in all dimensions, and thus the construction of accurate and more…
Optimal control of diffusion processes is intimately connected to the problem of solving certain Hamilton-Jacobi-Bellman equations. Building on recent machine learning inspired approaches towards high-dimensional PDEs, we investigate the…
We propose a hybridizable discontinuous Galerkin (HDG) method to approximate the solution of a distributed optimal control problem governed by an elliptic convection diffusion PDE. We derive optimal a priori error estimates for the state,…
The work is organized as follows. First an introduction is given in Chapter 1. In Chapter 2 we introduce the POD method in finite and infinite-dimensional Hilbert spaces and discuss various applications. Chapter 3 is devoted to to POD-based…
We prove convergence of the proximal policy gradient method for a class of constrained stochastic control problems with control in both the drift and diffusion of the state process. The problem requires either the running or terminal cost…