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Necessary optimality conditions and numerical methods for solving an optimal control problem for a linear continuous-time dynanical system with controlled coefficients and quadratic goal functional are discussed.

Optimization and Control · Mathematics 2010-04-20 Olga V. Baturina , Alexander V. Bulatov , Vadim F. Krotov

We propose a method to establish the rapid stabilization of the bilinear Schr\"odinger control system and its linearized system, and the finite time stabilization of the linearized system using the Grammian operators. The analysis of the…

Optimization and Control · Mathematics 2025-09-30 Hoai-Minh Nguyen

In this paper we study a bilinear optimal control problem associated to a 3D chemo-repulsion model with linear production. We prove the existence of weak solutions and we establish a regularity criterion to get global in time strong…

Optimization and Control · Mathematics 2018-08-29 Francisco Guillén-González , Exequiel Mallea-Zepeda , María Ángeles Rodríguez-Bellido

A basic idea in optimal transport is that optimizers can be characterized through a geometric property of their support sets called cyclical monotonicity. In recent years, similar "monotonicity principles" have found applications in other…

Optimization and Control · Mathematics 2023-08-31 Julio Backhoff-Veraguas , Mathias Beiglböck , Giovanni Conforti

In this paper a nonlinear coupled Schrodinger system in the presence of mixed cubic and superlinear power laws is considered. A non standard numerical method is developed to approximate the solutions in higher dimensional case. The idea…

Numerical Analysis · Mathematics 2018-05-16 Abdurahman F. Aljohani , Anouar Ben Mabrouk

In this work, we will investigate the question of optimal control for bilinear systems with constrained endpoint. The optimal control will be characterized through a set of unconstrained minimization problems that approximate the former.…

Optimization and Control · Mathematics 2021-07-28 Soufiane Yahyaoui , Lahoussine Lafhim , Mohamed Ouzahra

In this paper we study the bilinear-control problem for the linear and non-linear Schr{\"o}dinger equation with harmonic potential. By the means of different examples, we show how space-time smoothing effects (Strichartz estimates, Kato…

Analysis of PDEs · Mathematics 2020-01-22 Thomas Chambrion , Laurent Thomann

This paper focuses on the problem of quasi-periodic solutions for multi-dimensional quasi-linear Schr\"odinger equation. To address the challenge of unbounded perturbations caused by quasi-linear terms in the equation, we define the…

Dynamical Systems · Mathematics 2026-01-21 Zuhong You , Xiaoping Yuan

Optimizing the controls of quantum systems plays a crucial role in advancing quantum technologies. The time-varying noises in quantum systems and the widespread use of inhomogeneous quantum ensembles raise the need for high-quality quantum…

Quantum Physics · Physics 2025-05-06 Xinyu Fei , Lucas T. Brady , Jeffrey Larson , Sven Leyffer , Siqian Shen

We propose a new monotonically convergent algorithm which can enforce spectral constraints on the control field (and extends to arbitrary filters). The procedure differs from standard algorithms in that at each iteration the control field…

Quantum Physics · Physics 2015-05-13 M. Lapert , R. Tehini , G. Turinici , D. Sugny

We present a sufficient condition for approximate controllability of the bilinear discrete-spectrum Schr\"odinger equation exploiting the use of several controls. The controllability result extends to simultaneous controllability,…

Optimization and Control · Mathematics 2013-02-19 Ugo Boscain , Marco Caponigro , Mario Sigalotti

We analyze the qualitative properties and the order of convergence of a splitting scheme for a class of nonlinear stochastic Schr\"odinger equations driven by additive It\^o noise. The class of nonlinearities of interest includes nonlocal…

Numerical Analysis · Mathematics 2022-11-16 Charles-Edouard Bréhier , David Cohen

In this paper we present a constructive method to control the bilinear Schr\"odinger equation via two controls. The method is based on adiabatic techniques and works if the spectrum of the Hamiltonian admits eigenvalue intersections, and if…

Optimization and Control · Mathematics 2011-02-16 Ugo Boscain , Francesca Chittaro , Paolo Mason , Mario Sigalotti

A variety of physically relevant bilinear Schr\"odinger equations are known to be approximately controllable in large times. There are however examples which are approximately controllable in large times, but not in small times. This…

Optimization and Control · Mathematics 2025-06-24 Karine Beauchard , Eugenio Pozzoli

This note presents a sufficient condition for partial approximate ensemble controllability of a set of bilinear conservative quantum systems in an infinite dimensional Hilbert space. The proof relies on classical geometric and averaging…

Optimization and Control · Mathematics 2013-03-08 Thomas Chambrion

A major application of the mathematical concept of graph in quantum mechanics is to model networks of electrical wires or electromagnetic wave-guides. In this paper, we address the dynamics of a particle trapped on such a network in…

Optimization and Control · Mathematics 2023-04-19 Alessandro Duca

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…

Quantum Physics · Physics 2024-10-15 Xinyu Fei , Lucas T. Brady , Jeffrey Larson , Sven Leyffer , Siqian Shen

We consider a system described by a controlled bilinear Schr{\"o}dinger equation with three external inputs. We provide a constructive method to approximately steer the system from a given energy level to a superposition of energy levels…

Optimization and Control · Mathematics 2015-02-25 Paolo Mason , Francesca Chittaro

Discrete-time robust optimal control problems generally take a min-max structure over continuous variable spaces, which can be difficult to solve in practice. In this paper, we extend the class of such problems that can be solved through a…

Optimization and Control · Mathematics 2024-04-30 Jad Wehbeh , Eric C. Kerrigan

In this manuscript, we investigate optimal control problems which arise in connection with manipulation of dissipative quantum dynamics. These problems motivate the study of a class of dissipative bilinear control systems. For these systems…

Optimization and Control · Mathematics 2014-01-17 Dionisis Stefanatos , Navin Khaneja