Optimal control and sentinel applied to the parabolic systems
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Date
2021
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University of L’Arbi Ben M’hidi
Abstract
In this thesis, we were based on the analysis of controllability of parabolic system and sentinel theory.
We have shown that either regional or pointwise sentinel construction depends on the existence of optimal control.
The sentinel theory is given here in its more general and more realistic setting for Stockes problem and parabolic problems: in this case, the observation and the control have their supports in different open sets but not disjoint .
The problem of finding a sentinel is equivalent to anull-controllability problem for the parabolic equation that we solve.Elsewhere, the sentinel theory is an important tool in the estimation of the system pollution terms, independently of its missing terms.
Also we were concerned by the problem of identification of pollution terms which arise, first in Stockes problem and secondly in parabolic problem as for remote sensing problems, and which are modeled by a linear parabolic equation, using the new modification sentinel which change the classic definition of the sentinel method of J.-L.Lions (1992). A new modification of the sentinel is used to identify pollution terms in the general case where the observation and the control supports are disjoint.
2010 Mathematics Subject Classification : Primary 93B05; Secondary 93C20, 92D40.
Key words and phrases : Control Theory, Navier Stokes system with incomplete data, Turbulence Theory, Instantaneous Sentinel.
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Control Theory, Turbulence Theory, Instantaneous Sentinel