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IMA Journal of Mathematical Control and Information Advance Access originally published online on December 14, 2005
IMA Journal of Mathematical Control and Information 2006 23(1):1-9; doi:10.1093/imamci/dni016
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© The author 2005. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Controllability of the Ornstein–Uhlenbeck equation

Diomedes Bárcenas1, Hugo Leiva1,** and Wilfredo Urbina2

1 Departamento de Matemáticas, Universidad de Los Andes, Mérida 5101, Venezuela, 2 Departamento de Matemáticas, Facultad de Ciencias, Universidad Central de Venezuela, Apartado 47195, Los Chaguaramos, Caracas 1041-A, Venezuela

** Email: Leiva{at}ula.ve

In this paper we study the controllability of the following controlled Ornstein–Uhlenbeck equation

[graphic: see PDF]

then the system is approximately controllable on [0, t1]. Moreover, the system can never be exactly controllable.

Keywords: Ornstein–Uhlenbeck equation; approximate controllability; compact semigroup.


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