15 research outputs found
ON THE CONTROL OF ILL-POSED DISTRIBUTED PARAMETER SYSTEMS
International audienceWe show that the so-called low-regret (or least-regret) control by J. L. Lions [8] fits on the control of ill-posed problems. At each time, we give the characterization of the so-called no-regret control by means of singular optimality systems. For the backward heat ill-posed problem, no Slater hypothesis is assumed on the admissible set of controls U ad. This work is two pieces, and two methods are considered : the regularization method and the null-controllability method. For the first method, a zero order corrector is used, while for the second method, the passage to the limit is easy. The results presented here generalize the works in [2, 3] to the no-regret control. Résumé. On montre que le contrôlè a moindres regrets de J. L. Lions [8] est bien adapté pour le contrôle des desprobì emes mal posés. A chaque fois, on donne une caractérisation du contrôle sans regret par le moyen de systèmes d'optimalité singuliers. Pour leprobì eme de chaleur rétrograde mal posé, aucune hypothèse de type Slater sur l'ensemble des contrôles admissibles U ad n'est nécessaire. Ce travail est divisé en deux parties, et deux méthodes sont considérées: la méthode de régularisation et celle de la contrôlabilitécontrôlabilitéà zéro. Pour lapremì ere méthode, un correcteur d'ordre zéro est utilisé, alors que pour la seconde méthode le passagè a la limite est simple. Les résultats présentés ici généralisent les travaux dans [2, 3] au contrôle sans regret
A method for detecting pollution in dissipative systems with incomplete data.
Modelling environmental problems leads to mathematical
systems with missing data. For instance, weather problems
have generally missing initial conditions. The paper is
concerned with identifying pollution terms arising in the
state equation of some dissipative system with incomplete
initial condition.
To this aim the so-called sentinel method is used. Here,
the problem of determining a sentinel is equivalent to a
null-controllability problem for which Carleman inequalities
are revisited
Low-regret control of singular distributed systems: The Ill-posed backwards heat problem
International audienc