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SUMMARY:Asymptotic ensemble stabilization of the Bloch equation par F.C.Ch
ittaro (Toulon)
DTSTART;VALUE=DATE-TIME:20190206T120000Z
DTEND;VALUE=DATE-TIME:20190206T130000Z
DTSTAMP;VALUE=DATE-TIME:20200714T081221Z
UID:indico-event-4384@indico.math.cnrs.fr
DESCRIPTION:The notion of ensemble controllability (also called simulta
neous controllability) concerns the controllability of parametrized famili
es (ensembles) of control systems\, from some initial state to some prescr
ibed target state\, with the same control for the whole family. This issue
is motivated by recent engineering applications\, such as\, for instance\
, quantum control and distributed parameters systems.\n\nIn this talk\, we
are concerned with the simultaneous control of an ensemble of spin immers
ed in a magnetic field B(r\,t)\; in this model\, each spin is described
by the magnetization vector M ∈ R3\, subject to the dynamics ∂M =
B × M (Bloch equation).\n\nWe consider the case in which the z-comp
onent of the magnetic field is constant and non- uniform with respect to t
he position of the spins\, while the other two components are uniform and
can be controlled.\n\nCoupling a Lyapunov function approach with some tool
s of dynamical systems theory\, we exhibit a control function (in feedbac
k form) that approximately drives\, asymptotically in time and genericall
y with respect to the initial conditions\, all spins to the “down” pos
ition.\n\nTwo cases are addressed: if the set of spins is finite\, our st
rategy provides exact exponential stabilizability in infinite time\, whil
e if we have a countable collection of spins\, our approach implies asympt
otic pointwise convergence towards the target state.\n\nhttps://indico.mat
h.cnrs.fr/event/4384/
LOCATION:IMB 318
URL:https://indico.math.cnrs.fr/event/4384/
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