相关论文: A Posteriori Error Analysis for the Optimal Contro…

To address the magnetization dynamics in ferromagnetic materials described by the Landau-Lifshitz-Gilbert equation under large damping parameters, a third-order accurate numerical scheme is developed by building upon a second-order method…

Infinite horizon open loop optimal control problems for semilinear parabolic equations are investigated. The controls are subject to a cost-functional which promotes sparsity in time. The focus is put on deriving first order optimality…

We show that mean field optimal controls satisfy a first order optimality condition (at a.e. time) without any a priori requirement on their spatial regularity. This principle is obtained by a careful limit procedure of the Pontryagin…

A posteriori error estimates are an important tool to bound discretization errors in terms of computable quantities avoiding regularity conditions that are often difficult to establish. For non-linear and non-differentiable problems,…

Nowadays, a posteriori error control methods have formed a new important part of the numerical analysis. Their purpose is to obtain computable error estimates in various norms and error indicators that show distributions of global and local…

This paper is concerned with the design of optimal control for finite-dimensional control-affine nonlinear dynamical systems. We introduce an optimal control problem that specifically optimizes nonlinear observability in addition to…

We propose a mean-field optimal control problem for the parameter identification of a given pattern. The cost functional is based on the Wasserstein distance between the probability measures of the modeled and the desired patterns. The…

We consider an optimal control problem governed by an elliptic variational inequality of the second kind. The problem is discretized by linear finite elements for the state and a variational discrete approach for the control. Based on a…

We consider the variational discretization of a linear-quadratic optimal control problem with pointwise control and state constraints. In order to allow for a Fr\'echet smooth norm, the problem is reformulated by means of a reflexive…

We show how a posteriori goal oriented error estimation can be used to efficiently solve the subproblems occurring in a Model Predictive Control (MPC) algorithm. In MPC, only an initial part of a computed solution is implemented as a…

A posteriori error analysis is a technique to quantify the error in particular simulations of a numerical approximation method. In this article, we use such an approach to analyze how various error components propagate in certain moving…

This paper is concerned with an optimal control problem governed by a non-smooth semilinear elliptic equation. We show that the control-to-state mapping is directionally differentiable and precisely characterize its Bouligand…

In this paper we prove necessary conditions for optimality of a stochastic control problem for a class of stochastic partial differential equations that is controlled through the boundary. This kind of problems can be interpreted as a…

We devise an a posteriori error estimator for an affine optimal control problem subject to a semilinear elliptic PDE and control constraints. To approximate the problem, we consider a semidiscrete scheme based on the variational…

In this paper, we propose a novel approximation strategy for time-dependent hyperbolic systems of conservation laws for the Euler system of gas dynamics that aims to represent the dynamics of strong interacting discontinuities. The goal of…

We prove a general existence result in stochastic optimal control in discrete time where controls take values in conditional metric spaces, and depend on the current state and the information of past decisions through the evolution of a…

This paper studies a kind of minimal time control problems related to the exact synchronization for a controlled linear system of parabolic equations. Each problem depends on two parameters: the bound of controls and the initial state. The…

We apply innovative mathematical tools coming from optimal control theory to improve theoretical and experimental techniques in Magnetic Resonance Imaging (MRI). This approach allows us to explore and to experimentally reach the physical…

In this paper we present and analyze a weighted residual a posteriori error estimate for an optimal control problem. The problem involves a nondifferentiable cost functional, a state equation with an integral fractional Laplacian, and…

In this paper, an optimal control problem governed by a class of p-Laplacian elliptic equations is studied. In particular, as no monotonicity assumption is assumed on the nonlinear term, the state equation may admit several solutions for…