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We investigate the application of a posteriori error estimates to a fractional optimal control problem with pointwise control constraints. Specifically, we address a problem in which the state equation is formulated as an integral form of…

Optimization and Control · Mathematics 2023-10-10 Fangyuan Wang , Qiming Wang , Zhaojie Zhou

Optimal Dirichlet boundary control for a fractional/normal evolution with a final observation is considered. The unique existence of the solution and the first-order optimality condition of the optimal control problem are derived. The…

Numerical Analysis · Mathematics 2020-07-20 Qin Zhou , Binjie Li

We consider standard tracking-type, distributed elliptic optimal control problems with $L^2$ regularization, and their finite element discretization. We are investigating the $L^2$ error between the finite element approximation $u_{\varrho…

Numerical Analysis · Mathematics 2022-07-12 Ulrich Langer , Richard Löscher , Olaf Steinbach , Huidong Yang

This paper is concerned with the discretization error analysis of semilinear Neumann boundary control problems in polygonal domains with pointwise inequality constraints on the control. The approximations of the control are piecewise…

Numerical Analysis · Mathematics 2015-05-12 Johannes Pfefferer , Klaus Krumbiegel

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…

Numerical Analysis · Mathematics 2018-10-09 Jerome Droniou , Neela Nataraj , Devika Shylaja

This article is concerned with the nonconforming finite element method for distributed elliptic optimal control problems with pointwise constraints on the control and gradient of the state variable. We reduce the minimization problem into a…

Numerical Analysis · Mathematics 2021-12-13 Kamana Porwal , Pratibha Shakya

Optimal control of the singular nonlinear parabolic PDE which is a distributional formulation of multidimensional and multiphase Stefan-type free boundary problem is analyzed. Approximating sequence of finite-dimensional optimal control…

Analysis of PDEs · Mathematics 2020-06-16 Ugur G. Abdulla , Evan Cosgrove

The present paper addresses the topic of boundary output feedback stabilization of parabolic-type equations, governed by linear differential operators which can be diagonalized by the introduction of adequate weighting functions (by means…

Optimization and Control · Mathematics 2023-02-27 Hugo Lhachemi , Ionut Munteanu , Christophe Prieur

This paper develops and analyses numerical approximation for linear-quadratic optimal control problem governed by elliptic interface equations. We adopt variational discretization concept to discretize optimal control problem, and apply an…

Numerical Analysis · Mathematics 2018-06-04 Chao Chao Yang , Tao Wang , Xiaoping Xie

This paper is concerned with approximations and related discretization error estimates for the normal derivatives of solutions of linear elliptic partial differential equations. In order to illustrate the ideas, we consider the Poisson…

Numerical Analysis · Mathematics 2018-04-17 J. Pfefferer , M. Winkler

We present a numerical approximation method for linear diffusion-reaction problems with possibly discontinuous Dirichlet boundary conditions. The solution of such problems can be represented as a linear combination of explicitly known…

Numerical Analysis · Mathematics 2017-07-05 Ramona Baumann , Thomas P. Wihler

We consider a controlled state equation of parabolic type on the halfline $(0,+\infty)$ with boundary conditions of Dirichlet type in which the unknown is equal to the sum of the control and of a white noise in time. We study finite horizon…

Probability · Mathematics 2013-04-10 Federica Masiero

This paper addresses the problem of input-to-state stabilization for a class of parabolic equations with time-varying coefficients, as well as Dirichlet and Robin boundary disturbances. By using time-invariant kernel functions, which can…

Optimization and Control · Mathematics 2024-06-18 Yongchun Bi , Jun Zheng , Guchuan Zhu

This work addresses an optimal control problem constrained by a degenerate kinetic equation of parabolic-hyperbolic type. Using a hypocoercivity framework we establish the well-posedness of the problem and demonstrate that the optimal…

Numerical Analysis · Mathematics 2024-12-17 Aaron Pim , Tristan Pryer , Alex Trenam

We adopt the integral definition of the fractional Laplace operator and study an optimal control problem on Lipschitz domains that involves a fractional elliptic partial differential equation (PDE) as state equation and a control variable…

Numerical Analysis · Mathematics 2024-02-14 Francisco Bersetche , Francisco Fuica , Enrique Otarola , Daniel Quero

We study the robust output regulation of linear boundary control systems by constructing extended systems. The extended systems are established based on solving static differential equations under two new conditions. We first consider the…

Optimization and Control · Mathematics 2021-04-19 Duy Phan , Lassi Paunonen

This paper analyzes two eXtended finite element methods (XFEMs) for linear quadratic optimal control problems governed by Poisson equation in non-convex domains. We follow the variational discretization concept to discretize the continuous…

Numerical Analysis · Mathematics 2018-08-06 Tao Wang , Chao Chao Yang , Xiaoping Xie

We consider a linear-quadratic elliptic optimal control problem with point evaluations of the state variable in the cost functional. The state variable is discretized by conforming linear finite elements. For control discretization, three…

Numerical Analysis · Mathematics 2018-02-09 Niklas Behringer , Dominik Meidner , Boris Vexler

The purpose of this work is to study an optimal control problem for a semilinear elliptic partial differential equation with a linear combination of Dirac measures as a forcing term; the control variable corresponds to the amplitude of such…

Optimization and Control · Mathematics 2023-07-04 Enrique Otarola

We discretize a risk-neutral optimal control problem governed by a linear elliptic partial differential equation with random inputs using a Monte Carlo sample-based approximation and a finite element discretization, yielding finite…

Optimization and Control · Mathematics 2023-11-10 Johannes Milz