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We consider optimal control of fractional in time (subdiffusive, i.e., for $% 0<\gamma <1$) semilinear parabolic PDEs associated with various notions of diffusion operators in an unifying fashion. Under general assumptions on the…

Optimization and Control · Mathematics 2021-10-08 Harbir Antil , Ciprian G. Gal , Mahamadi Warma

We consider the null-controllability problem for the generalized Baouendi-Grushin equation $(\partial_t - \partial_x^2 - q(x)^2\partial_y^2)f = 1_\omega u$ on a rectangular domain. Sharp controllability results already exist when the…

Optimization and Control · Mathematics 2022-07-08 Jérémi Dardé , Armand Koenig , Julien Royer

We study the boundary control problems for the wave, heat, and Schr\"odinger equations on a finite graph. We suppose that the graph is a tree (i.e., it does not contain cycles), and on each edge an equation is defined. The control is acting…

Optimization and Control · Mathematics 2025-05-28 S. A. Avdonin , V. S. Mikhaylov

The question of controllability is investigated for a quantum control system in which the Hamiltonian operator components carry explicit time dependence which is not under the control of an external agent. We consider the general situation…

Quantum Physics · Physics 2009-11-10 Chunhua Lan , Tzyh-Jong Tarn , Quo-Shin Chi , John W. Clark

In this paper we introduce a new dynamical condition, the comb geometric control condition, which is sufficient for observability of the Schr\"odinger equation in Euclidean space. We provide examples which show this condition is strictly…

Analysis of PDEs · Mathematics 2026-04-14 Walton Green , Perry Kleinhenz

We study controllability of $d$-dimensional defocusing cubic Schroedinger equation under periodic boundary conditions. The control is applied additively, via a source term, which is a linear combination of few complex exponentials (modes)…

Optimization and Control · Mathematics 2011-11-16 Andrey Sarychev

We study a linear-quadratic optimal control problem involving a parabolic equation with fractional diffusion and Caputo fractional time derivative of orders $s \in (0,1)$ and $\gamma \in (0,1]$, respectively. The spatial fractional…

Optimization and Control · Mathematics 2015-04-02 Harbir Antil , Enrique Otarola , Abner J. Salgado

This paper aims to address an interesting open problem, posed in the paper "Singular Optimal Control for a Transport-Diffusion Equation" of Sergio Guerrero and Gilles Lebeau in 2007. The problem involves studying the null controllability…

Optimization and Control · Mathematics 2024-12-24 Fouad Et-Tahri , Jon Asier Bárcena-Petisco , Idriss Boutaayamou , Lahcen Maniar

The control-affine Schr\"odinger bridge concerns with a stochastic optimal control problem. Its solution is a controlled evolution of joint state probability density subject to a control-affine It\^o diffusion with a given deadline…

In this work, we investigate the $L^p$- partial null controllability of the abstract semilinear fractional-order differential inclusion with nonlocal conditions. The set of admissible controls is characterized by $u\in L^p(I,U)$,…

Optimization and Control · Mathematics 2025-05-07 Bholanath Kumbhakar , Deeksha , Dwijendra Narain Pandey

This analysis is concerned with the controllability of quantum systems in the case where the standard dipolar approximation, involving the permanent dipole moment of the system, is corrected with a polarizability term, involving the field…

Analysis of PDEs · Mathematics 2014-06-17 Nabile Boussaid , Marco Caponigro , Thomas Chambrion

This paper is concerned with the concepts of regional controllability for the Riemann-Liouville time fractional diffusion systems of order $\alpha\in(0,1)$. The characterizations of strategic actuators to achieve regional controllability…

Optimization and Control · Mathematics 2016-08-09 Fudong Ge , YangQuan Chen , Chunhai Kou

A new class of cost functionals for optimal control of quantum systems which produces controls which are sparse in frequency and smooth in time is proposed. This is achieved by penalizing a suitable time-frequency representation of the…

Optimization and Control · Mathematics 2016-07-15 Gero Friesecke , Felix Henneke , Karl Kunisch

The distributed null controllability for coupled parabolic systems with non-diagonalizable diffusion matrices with a reduced number of controls has been studied in the case of constant matrices. On the other hand, boundary controllability…

Optimization and Control · Mathematics 2022-09-09 Michel Duprez , Manuel González-Burgos , Diego A. Souza

Strichartz estimates, well-posedness theory and long time behavior for (nonlinear) Schr\"odinger equations on waveguide manifolds $\mathbb{R}^m \times \mathbb{T}^n$ are intensively studied in recent decades while the corresponding control…

Analysis of PDEs · Mathematics 2025-02-20 Jingrui Niu , Zehua Zhao

We consider semidiscrete finite differences schemes for the periodic Scr\"odinger equation in dimension one. We analyze whether the space-time integrability properties observed by Bourgain in the continuous case are satisfied at the…

Analysis of PDEs · Mathematics 2019-10-15 Liviu I. Ignat

We study the null-controllability properties of a one-dimensional wave equation with memory associated with the fractional Laplace operator. The goal is not only to drive the displacement and the velocity to rest at some time-instant but…

Analysis of PDEs · Mathematics 2019-01-30 Umberto Biccari , Mahamadi Warma

We prove global internal controllability in large time for the nonlinear Schrodinger equation on a bounded interval with periodic, Dirichlet or Neumann conditions. Our strategy combines stabilization and local controllability near 0. We use…

Analysis of PDEs · Mathematics 2008-12-18 Camille Laurent

In this paper we are concerned with the approximate controllability of a multidimensional semilinear reaction-diffusion equation governed by a multiplicative control, which is locally distributed in the reaction term. For a given initial…

Optimization and Control · Mathematics 2020-06-26 Mohamed Ouzahra

This paper discusses the approximate controllability of a fractional differential control problem driven by a nonlinear hemivariational inequality in a Hilbert space. First, we prove the existence of a mild solution for a fractional control…

Optimization and Control · Mathematics 2024-12-03 Garima Gupta , Jaydev Dabas