Displaying similar documents to “Exact distributed controllability for the semilinear wave equation.”

Controllability of Schrödinger equations

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...

Exact controllability of the 1-d wave equation from a moving interior point

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.

Controllability of partial differential equations on graphs

Sergei Avdonin, Victor Mikhaylov (2008)

Applicationes Mathematicae

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We study boundary control problems for the wave, heat, and Schrödinger 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 through the Dirichlet condition applied to all or all but one boundary vertices. Exact controllability in L₂-classes of controls is proved and sharp estimates of the time of controllability are obtained for the wave equation. Null controllability for the...

A theorem on the controllability of pertubated linear control systems

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.

Exact boundary controllability of a nonlinear KdV equation with critical lengths

Jean-Michel Coron, Emmanuelle Crépeau (2004)

Journal of the European Mathematical Society

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We study the boundary controllability of a nonlinear Korteweg–de Vries equation with the Dirichlet boundary condition on an interval with a critical length for which it has been shown by Rosier that the linearized control system around the origin is not controllable. We prove that the nonlinear term gives the local controllability around the origin.

Exact controllability of the radial solutions of the semilinear wave equation in R.

Luz de Teresa (1998)

Revista Matemática Complutense

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The exact internal controllability of the radial solutions of a semilinear heat equation in R is proved. The result applies for nonlinearities that are of an order smaller than |s| logp |s| at infinity for 1 ≤ p < 2. The method of the proof combines HUM and a fixed point technique.

Alternate checking criteria for reachable controllability of rectangular descriptor systems

Vikas Kumar Mishra, Nutan Kumar Tomar (2017)

Kybernetika

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Contrary to state space systems, there are different notions of controllability for linear time invariant descriptor systems due to the non smooth inputs and inconsistent initial conditions. A comprehensive study of different notions of controllability for linear descriptor systems is performed. Also, it is proved that reachable controllability for general linear time invariant descriptor system is equivalent to the controllability of some matrix pair under an assumption milder than...