Optimal Control and Time Scales

Reports



Moyennisation et Contrôle optimal
In this report (in French), it is shown that the asymptotic averaging results of the original
SIAM Paper can be rewritten as an error estimate involving a simple windowed averaging scheme.
Averaging on simple windows in deterministic optimal control
An updated version (in english) of this work.

Wavelets and Differentiation
A result by
Lemarié is recalled and it is shown that Daubechies biorthogonal wavelets, as a class, are invariant by differentiation, and are related by the differentiation/(de)convolution of Lemarié (with Sylvain Faure).
On rappelle le résultat de Lemarié et on montre que la classe des ondelettes splines biorthogonales présentée par Daubechies est invariante par différentiation, avec une relation très simple sur les indices déterminant les filtres. (avec S. Faure).

Product Invariant Piecewise Polynomial Approximations of Signals
A computational reference for the l'
ATA article. In particular, it describes two methods to obtain a piecewise of smooth signals from their scaling coefficients.

Calcul récursif de frame inverse sur la transformée en ondelettes dyadique
The detailed report (in french) corresponding to the
CDC 2001 conference paper.