RecentadvencesinaveragedcontrillabilityofhyperbolicPDEs

Abstract

The aim of this memory is to study the averagedcontrollability for parameter-dependentsystems. Wediscuss the notion of averaged control which has been introducedrecently by E.Zauzua . Weapply the method HUM whereitisbased on uniquenesscriteria (the direct and inverse inequalities) to somehyperbolicequationswith an unknownparameter. First, we consider the problem of controllability for linear finite and infinite dimensional systems and we give the averaged rank condition for averaged controllability. Secondly, westudy the averagedcontrollability of waveequationdepending on a parameterwhen the control isapplied on the boundary, by using the Hilbert Uniqueness Method (the method HUM) which has been introduced by J.L. Lions, wherethismethodallows us to design the avraged control of ourparameter-dependentwaveequation. Finally, westudywith the same argument of the HUM method the problem of vibrating plate equationdepending on a parameterwhen the control isapplied on the boundaryalso