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DTSTAMP:20220516T103313
DTSTART;TZID=Europe/Zurich:20220520T110000
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SUMMARY:Seminar in Numerical Analysis: Jens Saak (Max Planck Institute for Dynamics of Complex Technical Systems)
LOCATION:
DESCRIPTION:Optimal control problems subject to constraints given by partia
l differential equations are a powerful tool for the improvemen
t of many tasks in science an technology. Classic optimization
today is applicable on various problems and tackling nonlinear
equations and inclusion of box constraints on the solutions is
flexible. However, especially for non-stationary problems, smal
l perturbations along the trajectories can easily lead to large
deviations in the desired solutions. Consequently, optimality
may be lost just as easily. On the other hand, the linear-quadr
atic regulator problem in system theory is an approach to make
a dynamical system react to perturbation via feedback controls
that can be expressed by the solutions of matrix Riccati equati
ons. Itâ€™s applicability is limited by the linearity of the dy
namical system and the efficient solvability of the quadratic m
atrix equation. In this talk, we discuss how certain classes of
non-stationary PDEs can be reformulated (after spatial semi-di
scretization) into structured linear dynamical systems that all
ow the Riccati feedback to be computed. This allows us to combi
ne both approaches and thus steer solutions of perturbed PDEs b
ack to the optimized trajectories. The key to efficient solvers
for the Riccati equations is the usage of the specific structu
re in the problems and the fact that the Riccati solutions usua
lly feature a strong singular value decay, and thus good low-ra
nk approximability.\r\nFor further information about the semina
r, please visit this webpage [https://dmi.unibas.ch/en/research
/mathematics/seminar-in-numerical-analysis/].
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