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Theses

Equation de Riccati et contrôle de systèmes gouvernés par des équations aux dérivées partielles

Abstract : The results of this thesis are motivated by the developpement of the mathematical and numerical analysis technics for the control of systems governed by partial differential equation. After a recall about the LQR problem (and the associated Riccati's equation) in the case where the control operator is bounded, we consider this LQR problem in the case where the control operator is unbounded. We give an exemple of the pathological phenomena related to this case. A second part deals with the study of an irrigation channel. This part involves the modelisation of the problem (thanks to the Saint-Venant's equations), the theoretical study of the linearised problem and last, a numerical study. In the numerical study, we look in details how to obtain a feedback control that is robust at some perturbation of the system (H[exponent infinite]control). Finally, in a third part, we show that a class of non linear system is null controllable with a feedback control, infinite time. Moreover, this feedback is the same as the one used for the associated linear system.
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Theses
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http://docnum.univ-lorraine.fr/prive/SCD_T_2002_0277_CHAPELON.pdf
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https://hal.univ-lorraine.fr/tel-01746793
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Submitted on : Thursday, March 29, 2018 - 10:44:56 AM
Last modification on : Tuesday, March 2, 2021 - 5:12:06 PM

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Antoine Chapelon. Equation de Riccati et contrôle de systèmes gouvernés par des équations aux dérivées partielles. Mathématiques générales [math.GM]. Université Henri Poincaré - Nancy 1, 2002. Français. ⟨NNT : 2002NAN10277⟩. ⟨tel-01746793⟩

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