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CATEGORIES:CUED Control Group Seminars
SUMMARY:Graphical Nonlinear System Analysis - Tom Chaffey\
, University of Cambridge
DTSTART;TZID=Europe/London:20210617T140000
DTEND;TZID=Europe/London:20210617T150000
UID:TALK161089AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/161089
DESCRIPTION:Scaled relative graphs (SRGs) were recently introd
uced by Ryu\, Hannah and Yin to analyze the conver
gence of optimization algorithms using two dimensi
onal Euclidean geometry. In this seminar\, I’ll sh
ow how the SRG can be used to study incremental in
put/output properties of feedback systems. The SRG
of an LTI transfer function is the convex hull of
its Nyquist diagram under a particular change of
coordinates. The SRG may be plotted or approximate
d for arbitrary nonlinear operators\, and allows c
lassical Nyquist techniques to be applied to nonli
near systems. System interconnection corresponds t
o graphical manipulations of the systems’ SRGs. I
will give a generalization of the Nyquist criterio
n for stable systems\, where the Nyquist diagram a
nd the point −1 are replaced by SRGs of two feedba
ck-interconnected nonlinear operators. This theore
m encompasses the incremental small gain and passi
vity theorems\, and mixed small gain/passivity the
orems. The distance between the two SRGs is a nonl
inear stability margin\, and is the reciprocal of
the incremental gain of the feedback system. SRGs
can be over-approximated based on system propertie
s such as passivity and incremental gain\, and can
be plotted precisely for some static nonlineariti
es. I will provide an analytical calculation of th
e saturation function\, and show how SRG analysis
of Lur’e systems gives advantages over classical t
ools ranging from the circle criterion to IQC anal
ysis.\n\nZoom link:\nhttps://zoom.us/j/96507147724
LOCATION:Online (Zoom)
CONTACT:Thiago Burghi
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