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CATEGORIES:CUED Control Group Seminars
SUMMARY:Verifying stability of approximate explicit MPC -
Professor Morten Hovd (Deparment of Engineering Cy
bernetics\, Norwegian University of Science and Te
chnology)
DTSTART;TZID=Europe/London:20091127T140000
DTEND;TZID=Europe/London:20091127T150000
UID:TALK20574AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/20574
DESCRIPTION:Explicit MPC can potentially be used for safety cr
itical applications\, including applications to sy
stems with fast dynamics. Unfortunately\, the off
-line calculations at the design stage may be exce
ssively demanding\, and the required table size to
represent the solution may also be unacceptable f
or some applications.\n\nSeveral authors have ther
efore proposed various approximations to the (exac
t\, optimal) explicit MPC. In approximate explici
t MPC one generally accepts some degree of sub-opt
imality in order to arrive at a simpler solution\,
requiring fewer regions (and therefore also a sma
ller look-up table). Key properties of a design p
rocedure for approximate explicit MPC are:\ni) It
should not be necessary to find the exact solution
first\, and\nii) It should be possible to ascerta
in the closed loop stability of the approximate so
lution.\nMost authors guarantee stability by start
ing from an MPC formulation that guarantees stabil
ity for the exact solution\, and then ensure that
the cost of the approximate solution is 'close' to
the cost of the exact solution. It can then be s
hown that the optimal\ncost function is also a Lya
punov function for the approximate solution.\n\nTh
e talk will focus on alternative approaches to gua
ranteeing stability of approximate explicit MPC.
Two such approaches will be presented:\ni) Refinin
g the approximate solution until it can be shown t
hat the cost function for the approximate solution
is a Lyapunov function.\nii) Using an LMI formula
tion to find a piecewise quadratic Lyapunov functi
on for the approximate solution.\nFor the LMI form
ulation\, a novel relaxation will be proposed. Nu
merical examples indicate that this new relaxation
is superior to the relaxation in common use for f
inding PWQ Lyapunov functions.
LOCATION:Cambridge University Engineering Department\, Lect
ure Theatre 2
CONTACT:Dr Guy-Bart Stan
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