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CATEGORIES:CUED Control Group Seminars
SUMMARY:SMALL\, MEDIUM\, LARGE: NONLINEAR SYSTEMS ANALYSIS
TOOLS USING SUM OF SQUARES - Dr Antonis Papachris
todoulou (University of Oxford)
DTSTART;TZID=Europe/London:20100209T140000
DTEND;TZID=Europe/London:20100209T150000
UID:TALK23126AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/23126
DESCRIPTION:The use of Linear Matrix Inequality and Semidefini
te Programming\ntechniques is very common in moder
n control systems analysis and\ndesign. At the sam
e time\, positive polynomials can help formulate a
\nlarge number of problems in robust control\, non
-linear control and\nnon-convex optimization – con
sider\, for example\, the use of Lyapunov\nfunctio
ns for stability analysis of equilibria of nonline
ar dynamical\nsystems. The fact that polynomial po
sitivity conditions can be\nformulated efficiently
in terms of Linear Matrix Inequalities opens up\n
new directions in nonlinear systems analysis and d
esign.\n\nIn this talk I will first present how id
eas from dynamical systems\,\npositive polynomials
and convex optimization can be used to analyze\nt
he stability\, robust stability\, performance and
robust performance of\nsystems described by nonlin
ear ODEs. I will also discuss briefly how\nhybrid/
switched systems and time-delay systems can be ana
lyzed before\ndescribing how other\, more interest
ing analysis questions can be\nanswered using thes
e tools.\n\nThis approach for systems analysis\, a
lthough entirely algorithmic\, is\ncurrently not s
calable to large system instances. To address this
\, I\nwill first consider the analysis of large-sc
ale networked systems and\ndiscuss how the system
structure (both the dynamics at the nodes and\nthe
topology of the underlying network) can help gene
rate robust\nfunctionality conditions that scale w
ith the system size. I will\nfinally talk about so
me of the most recent work on how to analyze\n“med
ium-sized” dynamical systems\, combining ideas fro
m graph\npartitioning and the theory of interconne
cted systems.\n
LOCATION: Cambridge University Engineering Department\, LR6
CONTACT:Dr Ioannis Lestas
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