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UID:f4a8bb0a8de22554307509792e2fd5f7
CATEGORIES:Applied and Computational Math Seminar
CREATED:20240404T040631
SUMMARY:Data-driven system analysis: Polynomial optimization meets Koopman
LOCATION:Hill 705
DESCRIPTION:Understanding the stability and long-term behavior of dynamical systems is 
 vital in numerous applications. These properties can be studied through Lya
 punov frameworks that, when the dynamics are governed by known polynomial m
 odels, can be implemented computationally using polynomial optimization. Bu
 t what if the model is not polynomial or, worse, not even known?In this tal
 k, I will show that polynomial optimization can be combined with extended d
 ynamic mode decomposition to perform system analysis directly from measured
  data. This is possible thanks to a connection between Lyapunov frameworks 
 and the Koopman operator. After introducing the basic theory behind this co
 nnection, I will show how data-driven system analysis can guarantee stabili
 ty and unravel chaotic dynamics on a range of examples.\n
X-ALT-DESC;FMTTYPE=text/html:<p><span style="border: 0px; font-style: normal; font-weight: 400; font-siz
 e: 15px; line-height: inherit; font-family: 'Segoe UI', 'Segoe UI Web (West
  European)', 'Segoe UI', -apple-system, BlinkMacSystemFont, Roboto, 'Helvet
 ica Neue', sans-serif; margin: 0px; padding: 0px; vertical-align: baseline;
  color: #242424; letter-spacing: normal; orphans: 2; text-align: start; tex
 t-indent: 0px; text-transform: none; widows: 2; word-spacing: 0px; white-sp
 ace: normal; background-color: #ffffff;">Understanding the stability and lo
 ng-term behavior of dynamical systems is vital in numerous applications. Th
 ese properties can be studied through Lyapunov frameworks that,&nbsp;</span
 ><span style="border: 0px; font-style: normal; font-weight: 400; font-size:
  15px; line-height: inherit; font-family: 'Segoe UI', 'Segoe UI Web (West E
 uropean)', 'Segoe UI', -apple-system, BlinkMacSystemFont, Roboto, 'Helvetic
 a Neue', sans-serif; margin: 0px; padding: 0px; vertical-align: baseline; c
 olor: #242424; letter-spacing: normal; orphans: 2; text-align: start; text-
 indent: 0px; text-transform: none; widows: 2; word-spacing: 0px; white-spac
 e: normal; background-color: #ffffff;">when the dynamics are governed by kn
 own polynomial models,&nbsp;</span><span style="border: 0px; font-style: no
 rmal; font-weight: 400; font-size: 15px; line-height: inherit; font-family:
  'Segoe UI', 'Segoe UI Web (West European)', 'Segoe UI', -apple-system, Bli
 nkMacSystemFont, Roboto, 'Helvetica Neue', sans-serif; margin: 0px; padding
 : 0px; vertical-align: baseline; color: #242424; letter-spacing: normal; or
 phans: 2; text-align: start; text-indent: 0px; text-transform: none; widows
 : 2; word-spacing: 0px; white-space: normal; background-color: #ffffff;">ca
 n be implemented computationally using polynomial optimization. But what if
  the model is not polynomial or, worse, not even known?</span><br style="co
 lor: #242424; font-family: 'Segoe UI', 'Segoe UI Web (West European)', 'Seg
 oe UI', -apple-system, BlinkMacSystemFont, Roboto, 'Helvetica Neue', sans-s
 erif; font-size: 15px; font-style: normal; font-weight: 400; letter-spacing
 : normal; orphans: 2; text-align: start; text-indent: 0px; text-transform: 
 none; widows: 2; word-spacing: 0px; white-space: normal; background-color: 
 #ffffff;"><span style="color: #242424; font-family: 'Segoe UI', 'Segoe UI W
 eb (West European)', 'Segoe UI', -apple-system, BlinkMacSystemFont, Roboto,
  'Helvetica Neue', sans-serif; font-size: 15px; font-style: normal; font-we
 ight: 400; letter-spacing: normal; orphans: 2; text-align: start; text-inde
 nt: 0px; text-transform: none; widows: 2; word-spacing: 0px; white-space: n
 ormal; background-color: #ffffff; float: none;">In this talk, I will show t
 hat polynomial&nbsp;</span><span style="border: 0px; font-style: normal; fo
 nt-weight: 400; font-size: 15px; line-height: inherit; font-family: 'Segoe 
 UI', 'Segoe UI Web (West European)', 'Segoe UI', -apple-system, BlinkMacSys
 temFont, Roboto, 'Helvetica Neue', sans-serif; margin: 0px; padding: 0px; v
 ertical-align: baseline; color: #242424; letter-spacing: normal; orphans: 2
 ; text-align: start; text-indent: 0px; text-transform: none; widows: 2; wor
 d-spacing: 0px; white-space: normal; background-color: #ffffff;">optimizati
 on</span><span style="color: #242424; font-family: 'Segoe UI', 'Segoe UI We
 b (West European)', 'Segoe UI', -apple-system, BlinkMacSystemFont, Roboto, 
 'Helvetica Neue', sans-serif; font-size: 15px; font-style: normal; font-wei
 ght: 400; letter-spacing: normal; orphans: 2; text-align: start; text-inden
 t: 0px; text-transform: none; widows: 2; word-spacing: 0px; white-space: no
 rmal; background-color: #ffffff; float: none;">&nbsp;can be combined with&n
 bsp;</span><i style="color: #242424; font-family: 'Segoe UI', 'Segoe UI Web
  (West European)', 'Segoe UI', -apple-system, BlinkMacSystemFont, Roboto, '
 Helvetica Neue', sans-serif; font-size: 15px; font-weight: 400; letter-spac
 ing: normal; orphans: 2; text-align: start; text-indent: 0px; text-transfor
 m: none; widows: 2; word-spacing: 0px; white-space: normal; background-colo
 r: #ffffff;">extended dynamic mode decomposition</i><span style="color: #24
 2424; font-family: 'Segoe UI', 'Segoe UI Web (West European)', 'Segoe UI', 
 -apple-system, BlinkMacSystemFont, Roboto, 'Helvetica Neue', sans-serif; fo
 nt-size: 15px; font-style: normal; font-weight: 400; letter-spacing: normal
 ; orphans: 2; text-align: start; text-indent: 0px; text-transform: none; wi
 dows: 2; word-spacing: 0px; white-space: normal; background-color: #ffffff;
  float: none;">&nbsp;to perform system analysis directly from measured data
 . This is possible thanks to a connection between Lyapunov frameworks and t
 he Koopman operator. After introducing the basic theory behind this connect
 ion, I will show how data-driven system analysis can guarantee stability an
 d unravel chaotic dynamics on a range of examples.</span></p>
CONTACT:Giovanni Fantuzzi (Friedrich-Alexander-Universität Erlangen Nürnberg)
DTSTAMP:20260827T144204
DTSTART;TZID=America/New_York:20240408T110000
DTEND;TZID=America/New_York:20240408T120000
SEQUENCE:0
TRANSP:OPAQUE
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