Observabilité régionale du gradient des systèmes hyperboliques.

Abstract

The work realized in this thesis is a part of mathematics applied to the theoretical automatic. The concepts of regional analysis, internal and boundary, of the gradient were introduced for systems governed by hyperbolic equations. Various properties and characteristics are established, in particular in relation to the structure of the sensors. By use of the extending of the HUM method, we have established explicit expressions of the gradients of the initials states on the region w Ì W and which are exploitable from a numerical point of view. After, we have extended this study to the case where w is a part of the boundary ¶W . Algorithms for numerical implementation were developed and illustrated by various examples and which attest the success of the approach considered. The introduction of this concept is motivated by some reasons attached to the real problems.