Related papers: Space-time formulation, discretization, and comput…
This paper investigates a space-time interface-fitted approximation of a moving-interface optimal control problem with energy regularization. We reformulate the optimality conditions into a variational problem involving both the state and…
In this paper we consider a parabolic optimal control problem with a Dirac type control with moving point source in two space dimensions. We discretize the problem with piecewise constant functions in time and continuous piecewise linear…
We consider a fully discretized numerical scheme for parabolic stochastic partial differential equations with multiplicative noise. Our abstract framework can be applied to formulate a non-iterative domain decomposition approach. Such…
This work considers the problem of approximating initial condition and time-dependent optimal control and trajectory surfaces using multivariable Fourier series. A modified Augmented Lagrangian algorithm for translating the optimal control…
As a main step in the numerical solution of control problems in continuous time, the controlled process is approximated by sequences of controlled Markov chains, thus discretising time and space. A new feature in this context is to allow…
The numerical solution of time-dependent radiative transfer problems is challenging, both, due to the high dimension as well as the anisotropic structure of the underlying integro-partial differential equation. In this paper we propose a…
An optimal control problem related to the probability of transition between stable states for a thermally driven Ginzburg-Landau equation is considered. The value function for the optimal control problem with a spatial discretization is…
We establish a variety of results extending the well-known Pontryagin maximum principle of optimal control to discrete-time optimal control problems posed on smooth manifolds. These results are organized around a new theorem on critical and…
A classical approach for solving discrete time nonlinear control on a finite horizon consists in repeatedly minimizing linear quadratic approximations of the original problem around current candidate solutions. While widely popular in many…
This article solves an optimal control problem arising in attitude control of a spacecraft under state and control constraints. We first derive the discrete-time attitude dynamics by employing discrete mechanics. The orientation transfer,…
We propose an {\em implementable} numerical scheme for the discretization of linear-quadratic optimal control problems involving SDEs in higher dimensions with {\em control constraint}. For time discretization, we employ the implicit Euler…
We present an energy-preserving mechanic formulation for dynamic quasi-brittle fracture in an Eulerian-Lagrangian formulation, where a second-order phase-field equation controls the damage evolution. The numerical formulation adapts in…
We establish a Pontryagin maximum principle for discrete time optimal control problems under the following three types of constraints: a) constraints on the states pointwise in time, b) constraints on the control actions pointwise in time,…
The paper deals with a stochastic Galerkin approximation of elliptic Dirichlet boundary control problems with random input data. The expectation of a tracking cost functional with the deterministic constrained control is minimized. Error…
Many scientific and engineering challenges can be formulated as optimization problems which are constrained by partial differential equations (PDEs). These include inverse problems, control problems, and design problems. As a major…
In this work, we present a second-order numerical scheme to address the solution of optimal control problems constrained by the evolution of nonlinear Fokker-Planck equations arising from socio-economic dynamics. In order to design an…
This work presents and analyzes space-time finite element methods on fully unstructured simplicial space-time meshes for the numerical solution of parabolic optimal control problems. Using Babu\v{s}ka's theorem, we show well-posedness of…
In this paper, optimal control problems governed by diffusion equations with Dirichlet and Neumann boundary conditions are investigated in the framework of the gradient discretisation method. Gradient schemes are defined for the optimality…
This work discusses the finite element discretization of an optimal control problem for the linear wave equation with time-dependent controls of bounded variation. The main focus lies on the convergence analysis of the discretization…
We develop a convergence theory of space-time discretizations for the linear, 2nd-order wave equation in polygonal domains $\Omega\subset\mathbb{R}^2$, possibly occupied by piecewise homogeneous media with different propagation speeds.…