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SUMMARY:A deterministic least squares approach for simultaneous input and 
 state estimation  - Greg Gakis\, University of Cambridge
DTSTART:20211104T140000Z
DTEND:20211104T150000Z
UID:TALK165502@talks.cam.ac.uk
CONTACT:Thiago Burghi
DESCRIPTION:This paper considers a deterministic estimation problem to fin
 d the input and state of a linear dynamical system which minimises a weigh
 ted integral squared error between the resulting output and the measured o
 utput. 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 procedure that is reminiscent of the
  Kalman filter. The first stage is an end-of-interval estimator for the fi
 nite horizon which may be solved in real time as the horizon length increa
 ses. The second stage computes the unique optimum over a fixed horizon by 
 a backwards integration over the horizon. A related tracking problem is so
 lved in an analogous manner. Making use of the solution to both the estima
 tion and tracking problems a constrained estimation problem is solved whic
 h shows that the Riccati equation solution has a least squares interpretat
 ion that is analogous to the meaning of the covariance matrix in stochasti
 c filtering. The paper shows that the estimation and tracking problems con
 sidered here include the Kalman filter and the linear quadratic regulator 
 as special cases. The infinite horizon case is also considered for both th
 e estimation and tracking problems. Stability and convergence conditions a
 re provided and the optimal solutions are shown to take the form of left i
 nverses of the original system. 
LOCATION:LR 11\, Department of Engineering / Online (Zoom)
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