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Michał Kisielewicz (2002)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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Some sufficient conditions for controllability of nonlinear systems described by differential equation ẋ = f(t,x(t),u(t)) are given.
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.
Jerzy Klamka (2002)
International Journal of Applied Mathematics and Computer Science
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Local constrained controllability problems for nonlinear finite-dimensional discrete 1-D and 2-D control systems with constant coefficients are formulated and discussed. Using some mapping theorems taken from nonlinear functional analysis and linear approximation methods, sufficient conditions for constrained controllability in bounded domains are derived and proved. The paper extends the controllability conditions with unconstrained controls given in the literature to cover both 1-D...
Krishnan Balachandran (1988)
Kybernetika
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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...
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...
S. Guerrero, O. Yu. Imanuvilov (2007)
Annales de l'I.H.P. Analyse non linéaire
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