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CATEGORIES:CUED Control Group Seminars
SUMMARY:Analytical solutions\, duality and symmetry in con
strained control and estimation - Dr Jose De Dona
(The University of Newcastle\, Australia--on study
leave during 2008/2009 at Ecole des Mines de Pari
s\, France)
DTSTART;TZID=Europe/London:20090220T140000
DTEND;TZID=Europe/London:20090220T150000
UID:TALK14436AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/14436
DESCRIPTION:In this talk we will explore the interplay between
estimation and control problems for linear system
s with constraints. We will present results that e
xtend\, to the constrained case\, the well-known c
onnections that exist in the absence of constraint
s. For example\, for linear unconstrained systems\
, it is well known that the optimal quadratic regu
lator and the Kalman filter share a duality relati
onship\, where the different system and objective
function parameters can be interchanged according
to well defined relations. This duality relationsh
ip was established by R. Kalman and collaborators
in the 1960s\, and one important implication is th
at it allows for an exchange of solutions between
estimation and control problems. However\, the rel
ationships between control and estimation\, in the
constrained cases\, are—despite their importance
in practical applications— not as well understood.
The context of this talk will be that of Model Pr
edictive Control (MPC) and Moving Horizon Estimati
on (MHE)\, arguably the most popular methodologies
for dealing with constrained problems. We will fi
rst establish a Lagrangian duality relationship be
tween constrained state estimation and control\, a
nd show that the well-known unconstrained duality
relationship is a special case of our constrained
result. We will also see that both problems—const
rained estimation and control—exhibit a remarkable
symmetry in the light of this duality relationshi
p. The second result is concerned with the optimal
solution to both constrained problems\, which wil
l be derived analytically by using dynamic program
ming. The optimal solution is given by a piece-wis
e affine function of the data (or parameter). This
optimal solution— of course— coincides with the o
ne obtained by other existing methods belonging to
what is usually referred to as explicit solutions
in MPC and MHE. However\, the use of dynamic prog
ramming will allow us to derive the solutions—at l
east for simple constrained problems— in an entire
ly analytical way\, obtaining recursive equations
that can be interpreted as the constrained version
s of the Riccati equation. Finally\, we will revis
it the connection between constrained control and
estimation problems. We will show that\, from the
analytical solutions to both problems (obtained wi
th dynamic programming)\, a clear symmetry relatio
nship is exposed between them\, which is different
from the Lagrangian duality relationship. This no
vel symmetry is summarized by means of a translati
on table that gives a complete correspondence of a
ll variables of one problem into the variables of
the other.\n
LOCATION:Cambridge University Engineering Department\, Lect
ure Room 3B
CONTACT:Dr Guy-Bart Stan
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