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CATEGORIES:CUED Control Group Seminars
SUMMARY:Block Scaled Diagonal Dominance for Applications i
n Control Theory and Optimisation - Aivar Sootla\,
University of Oxford
DTSTART;TZID=Europe/London:20190221T140000
DTEND;TZID=Europe/London:20190221T150000
UID:TALK117778AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/117778
DESCRIPTION:In this talk\, we present a generalisation of scal
ed diagonally dominant (SDD) matrices to block par
titioned matrices as well as their applications in
control theory and optimisation. Our basic defini
tion of block SDD matrices relies on a comparison
matrix\, which is formed by computing particular n
orms of the blocks in the partitioning. If the com
parison matrix is stable then partitioned matrix i
s stable\, moreover\, there exists a block-diagona
l solution to Lyapunov inequality and the H infini
ty Riccati inequality. Furthermore\, these solutio
ns can be constructed using the combination of lin
ear algebra and linear programming methods. We the
n focus on symmetric matrices and introduce a set
of block factor-width-two matrices\, which can als
o be seen as a generalisation of SDD matrices. Blo
ck factor-width-two matrices form a proper cone\,
which is a subset of positive semidefinite matrice
s. We use these cones and their duals to build hie
rarchies of inner and outer approximations of the
cone of positive semidefinite matrices. The main f
eature of these cones is that they enable decompos
ition of a large semidefinite constraint into a nu
mber of smaller semidefinite constraints. As the m
ain application of this class of matrices\, we env
ision large-scale semidefinite feasibility optimis
ation programs including the sum-of-squares (SOS)
programs. We present numerical examples from SOS o
ptimisation showcasing the strengths of this decom
position.
LOCATION:Cambridge University Engineering Department\, Lect
ure Theatre 6
CONTACT:Alberto Padoan
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