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SUMMARY:SMALL\, MEDIUM\, LARGE: NONLINEAR SYSTEMS ANALYSIS TOOLS USING SUM
  OF SQUARES - Dr Antonis Papachristodoulou (University of Oxford)
DTSTART:20100209T140000Z
DTEND:20100209T150000Z
UID:TALK23126@talks.cam.ac.uk
CONTACT:Dr Ioannis Lestas
DESCRIPTION:The use of Linear Matrix Inequality and Semidefinite Programmi
 ng\ntechniques is very common in modern control systems analysis and\ndesi
 gn. At the same time\, positive polynomials can help formulate a\nlarge nu
 mber of problems in robust control\, non-linear control and\nnon-convex op
 timization – consider\, for example\, the use of Lyapunov\nfunctions for
  stability analysis of equilibria of nonlinear dynamical\nsystems. The fac
 t that polynomial positivity conditions can be\nformulated efficiently in 
 terms of Linear Matrix Inequalities opens up\nnew directions in nonlinear 
 systems analysis and design.\n\nIn this talk I will first present how idea
 s from dynamical systems\,\npositive polynomials and convex optimization c
 an be used to analyze\nthe stability\, robust stability\, performance and 
 robust performance of\nsystems described by nonlinear ODEs. I will also di
 scuss briefly how\nhybrid/switched systems and time-delay systems can be a
 nalyzed before\ndescribing how other\, more interesting analysis questions
  can be\nanswered using these tools.\n\nThis approach for systems analysis
 \, although entirely algorithmic\, is\ncurrently not scalable to large sys
 tem instances. To address this\, I\nwill first consider the analysis of la
 rge-scale networked systems and\ndiscuss how the system structure (both th
 e dynamics at the nodes and\nthe topology of the underlying network) can h
 elp generate robust\nfunctionality conditions that scale with the system s
 ize. I will\nfinally talk about some of the most recent work on how to ana
 lyze\n“medium-sized” dynamical systems\, combining ideas from graph\np
 artitioning and the theory of interconnected systems.\n
LOCATION: Cambridge University Engineering Department\, LR6
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