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DTSTAMP:20220525T171141Z
DESCRIPTION:Virtual Informal Systems Seminar (VISS)\n\nCentre for Intellige
nt Machines (CIM) and Groupe d'Etudes et de Recherche en Analyse des Decis
ions (GERAD)Zoom Link\n Meeting ID: 910 7928 6959 \n Passcode: VISS\n
Speaker: Emmanuel Trélat\, Professor\, Sorbonne Université\, Laboratoire J
acques-Louis Lions\, CNRS\n Abstract:\n I will first recall some results on
how to achieve consensus for well known classes of systems\, like the cele
brated Cucker-Smale or Hegselmann-Krause models. When the systems are symm
etric\, convergence to consensus is classically established by proving\, f
or instance\, that the usual variance is an exponentially decreasing Lyapu
nov function: this is a 'L^2 theory'. When the systems are not symmetric\,
no L^2 theory existed until now and convergence was proved by means of a
'L^\infty theory'.\n In this talk I will show how to develop a L^2 theory b
y designing an adequately weighted variance\, and how to obtain the sharp
rate of exponential convergence to consensus for general finite and infini
te-dimensional linear first-order consensus systems.\n If time allows\, I w
ill show applications in which one is interested in controlling vote behav
iors in an opinion model.\n Biography:\n Emmanuel Trélat is full professor a
t Sorbonne Université in Paris\, he is the director of Laboratoire Jacques
-Louis Lions. His interests range over control theory in finite and infini
te dimension\, optimal control\, stabilization\, geometry\, and numerical
issues. He has been awarded several prizes\, among which the Felix Klein P
rize by the EMS in 2012 for his achievements on the optimal guidance of Ar
iane launchers\, and has been an invited speaker at ICM in 2018. He is the
current editor in chief of the journal COCV (Control Calculus of Variatio
ns and Optimization). \n
DTSTART:20220114T150000Z
DTEND:20220114T160000Z
SUMMARY:Exponential convergence towards consensus for non-symmetric linear
first-order systems in finite and infinite dimensions
URL:https://www.mcgill.ca/cim/channels/event/exponential-convergence-toward
s-consensus-non-symmetric-linear-first-order-systems-finite-and-336094
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