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INICIO | 23 de mayo de 2024

A weak regularity theorem for real analytic optimal control problems.

Título inglés A weak regularity theorem for real analytic optimal control problems.
Título español Un teorema de regularidad débil para problemas reales de control óptimo analítico.
Autor/es Sussmann, Hector J.
Organización Math. Dep. Rutgers Univ., New Brunswick (New Jersey), Estados Unidos
Revista 0213-2230
Publicación 1986, 2 (3): 307-317, 19 Ref.
Tipo de documento articulo
Idioma Inglés
Resumen inglés We consider real analytic finite-dimensional control problems with a scalar input that enters linearly in the evolution equations. We prove that, whenever it is possible to steer a state x to another state y by means of a measurable control, then it is possible to steer x to y by means of a control that has an extra regularity property, namely, that of being analytic on an open dense subset of its interval of definition. Since open dense sets can have very small measure, this is a very weak property. However, it is absolutely general, depending on no assumptions other than real analyticity. This shows that real analyticity alone suffices to imply some regularity, and leaves open the question of how much more regularity can be proved in general. To show that real analiticity is essential, we prove, by constructing a class of examples, that no such theorem is true in the C case. The regularity result implies a similar regularity theorem for time-optimal controls.
Clasificación UNESCO 120219
Palabras clave español Ecuaciones diferenciales ordinarias ; Control óptimo
Código MathReviews MR0908055
Código Z-Math Zbl 0638.49018
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Equipo DML-E
Instituto de Ciencias Matemáticas (ICMAT - CSIC)