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This article presents a general and novel approach to the automation of goal-oriented error control in the solution of nonlinear stationary finite element variational problems. The approach is based on automated linearization to obtain the…
The minimization of operation costs for natural gas transport networks is studied. Based on a recently developed model hierarchy ranging from detailed models of instationary partial differential equations with temperature dependence to…
We investigate the numerical approximation of an elliptic optimal control problem which involves a nonconvex local regularization of the $L^q$-quasinorm penalization (with $q\in(0,1)$) in the cost function. Our approach is based on the…
We analyze space-time finite element methods for the numerical solution of distributed parabolic optimal control problems with energy regularization in the Bochner space $L^2(0,T;H^{-1}(\Omega))$. By duality, the related norm can be…
This note is concerned with an optimal control problem governed by the relativistic Maxwell-Newton-Lorentz equations, which describes the motion of charges particles in electro-magnetic fields and consists of a hyperbolic PDE system coupled…
This work is motivated by the need to study the impact of data uncertainties and material imperfections on the solution to optimal control problems constrained by partial differential equations. We consider a pathwise optimal control…
The article discusses the gradient discretisation method (GDM) for distributed optimal control problems governed by diffusion equation with pure Neumann boundary condition. Using the GDM framework enables to develop an analysis that…
In many high-frequency simulation workflows, eigenvalue tracking along a parameter variation is necessary. This can become computationally prohibitive when repeated time-consuming eigenvalue problems must be solved. Therefore, we employ a…
We propose a semi-discrete numerical scheme and establish well-posedness of a class of parabolic systems. Such systems naturally arise while studying the optimal control of grain boundary motions. The latter is typically described using a…
We introduce a max-plus analogue of the Petrov-Galerkin finite element method to solve finite horizon deterministic optimal control problems. The method relies on a max-plus variational formulation. We show that the error in the sup norm…
The considered optimal control problem of a stochastic power system, is to select the set of power supply vectors which infimizes the probability that the phase-angle differences of any power flow of the network, endangers the transient…
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…
We consider a stochastic control problem, where the control domain is convex and the system is governed by a nonlinear backward stochastic differential equation. With a L1 terminal data, we derive necessary optimality conditions in the form…
A general setup for deterministic system identification problems on graphs with Dirichlet and Neumann boundary conditions is introduced. When control nodes are available along the boundary, we apply a discretize-then-optimize method to…
In this article, we derive \textit{a posteriori} error estimates for the Dirichlet boundary control problem governed by Stokes equation. An energy-based method has been deployed to solve the Dirichlet boundary control problem. We employ an…
This paper is concerned with the distributed control and stabilization problems for linear discrete-time large scale systems with imposed constraints. The main contributions of this paper are: Firstly, by using the maximum principle…
This paper deals with partially-observed optimal control problems for the state governed by stochastic differential equation with delay. We develop a stochastic maximum principle for this kind of optimal control problems using a variational…
We study a multiscale stochastic optimal control problem subject to state constraints on the slow variable. To address this class of problems, we develop a rigorous theoretical framework based on singular perturbation analysis, tailored to…
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…
The main aim of this article is to analyze mixed finite element method for the second order Dirichlet boundary control problem. Therein, we develop both a priori and a posteriori error analysis using the energy space based approach. We…