Control norms for large control times
Sergei Ivanov (1999)
ESAIM: Control, Optimisation and Calculus of Variations
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Sergei Ivanov (1999)
ESAIM: Control, Optimisation and Calculus of Variations
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Benabdallah, Assia, Naso, Maria Grazia (2002)
Abstract and Applied Analysis
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J.-M. Coron (1992-1993)
Séminaire Équations aux dérivées partielles (Polytechnique)
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Karine Beauchard (2005-2006)
Séminaire Équations aux dérivées partielles
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One considers a quantum particle in a 1D moving infinite square potential well. It is a nonlinear control system in which the state is the wave function of the particle and the control is the acceleration of the potential well. One proves the local controllability around any eigenstate, and the steady state controllability (controllability between eigenstates) of this control system. In particular, the wave function can be moved from one eigenstate to another one, exactly and in finite...
Ornella Naselli Ricceri (1989)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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In this Note, applying our recent Theorem 3.1 of [7], we prove that suitable perturbations of a completely controllable linear control system, do not affect the controllability of the system.
Reinhard Illner, Horst Lange, Holger Teismann (2006)
ESAIM: Control, Optimisation and Calculus of Variations
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We give the definitions of exact and approximate controllability for linear and nonlinear Schrödinger equations, review fundamental criteria for controllability and revisit a classical “No-go” result for evolution equations due to Ball, Marsden and Slemrod. In Section 2 we prove corresponding results on non-controllability for the linear Schrödinger equation and distributed additive control, and we show that the Hartree equation of quantum chemistry with bilinear control is...
Ornella Naselli Ricceri (1989)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti
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In this Note, applying our recent Theorem 3.1 of [7], we prove that suitable perturbations of a completely controllable linear control system, do not affect the controllability of the system.
Liu, Wei-Jiu (2000)
Portugaliae Mathematica
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Carlos Castro (2013)
ESAIM: Control, Optimisation and Calculus of Variations
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We consider the linear wave equation with Dirichlet boundary conditions in a bounded interval, and with a control acting on a moving point. We give sufficient conditions on the trajectory of the control in order to have the exact controllability property.