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CATEGORIES:CUED Control Group Seminars
SUMMARY:A deterministic least squares approach for simulta
neous input and state estimation - Greg Gakis\, U
niversity of Cambridge
DTSTART;TZID=Europe/London:20211104T140000
DTEND;TZID=Europe/London:20211104T150000
UID:TALK165502AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/165502
DESCRIPTION:This paper considers a deterministic estimation pr
oblem to find the input and state of a linear dyna
mical system which minimises a weighted integral s
quared error between the resulting output and the
measured output. A completion of squares approach
is used to find the unique optimum in terms of the
solution of a Riccati differential equation. The
optimal estimate is obtained from a two-stage proc
edure that is reminiscent of the Kalman filter. Th
e first stage is an end-of-interval estimator for
the finite horizon which may be solved in real tim
e as the horizon length increases. The second stag
e computes the unique optimum over a fixed horizon
by a backwards integration over the horizon. A re
lated tracking problem is solved in an analogous m
anner. Making use of the solution to both the esti
mation and tracking problems a constrained estimat
ion problem is solved which shows that the Riccati
equation solution has a least squares interpretat
ion that is analogous to the meaning of the covari
ance matrix in stochastic filtering. The paper sho
ws that the estimation and tracking problems consi
dered here include the Kalman filter and the linea
r quadratic regulator as special cases. The infini
te horizon case is also considered for both the es
timation and tracking problems. Stability and conv
ergence conditions are provided and the optimal so
lutions are shown to take the form of left inverse
s of the original system.
LOCATION:LR 11\, Department of Engineering / Online (Zoom)
CONTACT:Thiago Burghi
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