Boundary controllability for the nonlinear Korteweg-de Vries equation on any critical domain

Eduardo Cerpa; Emmanuelle Crépeau

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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...

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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 $(E (t) \cdot x) u$ is...

A theorem on the controllability of pertubated linear control systems

Ornella Naselli Ricceri (1989)

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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.