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DTSTART:20221028T210000Z
UID:167179@events.unl.edu
DTSTAMP:20220831T222022Z
ORGANIZER;CN=Mikil Foss:
SUMMARY:Mahamadi Warma\, George Mason University
STATUS:CONFIRMED
DESCRIPTION:In this talk we consider averages convergence as the time-horiz
on goes to infinity of optimal solutions of time-dependent control problem
s to optimal solutions of the corresponding stationary optimal control pro
blems. Control problems play a key role in engineering\, economics\, and s
ciences. To be more precise\, in climate sciences\, often times\, relevant
problems are formulated in long time scales\, so that\, the problem of po
ssible asymptotic behaviors when the time-horizon goes to infinity becomes
natural. Assuming that the controlled dynamics under consideration are st
abilizable towards a stationary solution\, the following natural question
arises\: Do time averages of optimal controls and trajectories converge to
the stationary optimal controls and states as the time-horizon goes to in
finity? This question is very closely related to the so-called turnpike pr
operty that shows that\, often times\, the optimal trajectory joining two
points that are far apart\, consists in\, departing from the point of orig
in\, rapidly getting close to the steady-state (the turnpike) to stay ther
e most of the time\, to quit it only very close to the final destination a
nd time. In the present talk we are dealing with control problems of fract
ional parabolic equations with non-zero Dirichlet exterior data associated
with the fractional Laplace operator. We prove the turnpike property for
the non-local Dirichlet control problem.
LOCATION:Avery Hall Room 115
URL://events.unl.edu/math/2022/10/28/167179/
DTEND:20221028T215000Z
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