Related papers: Space-time finite element methods for distributed …
This article examines a linear-quadratic elliptic optimal control problem in which the cost functional and the state equation involve a highly oscillatory periodic coefficient $A^\varepsilon$. The small parameter $\varepsilon>0$ denotes the…
We consider linear model reduction in both the control and state variables for unconstrained linear-quadratic optimal control problems subject to time-varying parabolic PDEs. The first-order optimality condition for a state-space reduced…
In this article, we consider the Tikhonov regularization of an optimal control problem of semilinear partial differential equations with box constraints on the control. We derive a-priori regularization error estimates for the control under…
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 consider an elliptic optimal control problem where the objective functional contains evaluations of the state at a finite number of points. In particular, we use a fidelity term that encourages the state to take certain values at these…
In this article, we present an Unfitted Space-Time Finite Element method for the scalar transport equation posed on moving domains. We consider the case of the domain boundary being transported by the same velocity field as the scalar…
Leveraging the techniques found in the literature on Quantum Equilibration for finite dimensional systems, we develop the theory of Quantum Equilibration for the case of infinite-dimensional systems, particularly the cases where the…
The numerical analysis of a family of distributed mixed optimal control problems governed by elliptic variational inequalities (with parameter $\alpha >0$) is obtained through the finite element method when its parameter $h\rightarrow 0$.…
In this paper, a space-time discontinuous Galerkin finite element method for distributed optimal control problems governed by unsteady diffusion-convection-reaction equations with control constraints is studied. Time discretization is…
$L^2$ norm error estimates of semi- and full discretisations, using bulk--surface finite elements and Runge--Kutta methods, of wave equations with dynamic boundary conditions are studied. The analysis resides on an abstract formulation and…
In this article we study a finite horizon optimal control problem with monotone controls. We consider the associated Hamilton-Jacobi-Bellman (HJB) equation which characterizes the value function. We consider the totally discretized problem…
We study space--time isogeometric discretizations of the linear acoustic wave equation that use splines of arbitrary degree p, both in space and time. We propose a space--time variational formulation that is obtained by adding a…
We unify and extend the semigroup and the PDE approaches to stochastic maximal regularity of time-dependent semilinear parabolic problems with noise given by a cylindrical Brownian motion. We treat random coefficients that are only…
We consider finite element approximations of ill-posed elliptic problems with conditional stability. The notion of {\emph{optimal error estimates}} is defined including both convergence with respect to mesh parameter and perturbations in…
The purpose of this work is the design and analysis of a reliable and efficient a posteriori error estimator for the so-called pointwise tracking optimal control problem. This linear-quadratic optimal control problem entails the…
The paper introduces a new finite element numerical method for the solution of partial differential equations on evolving domains. The approach uses a completely Eulerian description of the domain motion. The physical domain is embedded in…
In various physical implementations of quantum information processing, qubits are realized in a Lambda type system configuration as two stable lower energy levels coupled indirectly via an unstable higher energy level, that is, in…
Quantum optimal control is a technique for controlling the evolution of a quantum system and has been applied to a wide range of problems in quantum physics. We study a binary quantum control optimization problem, where control decisions…
In this paper, we consider the problem of minimum-time optimal control for a dynamical system with initial state uncertainties and propose a sequential convex programming (SCP) solution framework. We seek to minimize the expected terminal…
This paper is concerned with optimal control problems for parabolic partial differential equations with pointwise in time switching constraints on the control. A standard approach to treat constraints in nonlinear optimization is…