## DYNAMICAL SYSTEMS Seminar

### On Data Assimilation through Variational Calculus

Jochen Broecker
(Max-Planck Institut for the Physics of Complex Systems)

Abstract: Time series are often assumed to arise as observations from an underlying dynamical system. The observations though need not be one--to--one mappings of the full state of the underlying dynamical system, which is thus only partially observed. Both for the purpose of analyzing such systems as well as forecasting future observations, it is usually necessary to compute trajectories which are on the one hand consistent with some proposed model of the dynamics, but which on the other hand closely follow (or shadow') the recent history of observations. This process (referred to as data assimilation in the atmospheric sciences or smoothing in the engineering community) is revisited in this talk. An approach to data assimilation using concepts from nonlinear control theory will be presented. The model dynamics are augmented by a control force, which is chosen so as to make the discrepancy between the trajectory and the actual observations, the tracking error, small. At the same time, large control actions are penalized as well, in order to create trajectories which are as consistent with the (uncontrolled) model dynamics as possible. Provided there is no model error, the control is expected to vanish once the dynamics is `on track''. In the presence of model error though, a small but non-vanishing control will remain necessary to keep the trajectory close to the observations. It is demonstrated that this approach provides an effective means to regularize the problem, and to control the trade-off between perfectly following the observations and perfectly obeying the model dynamics.

Wednesday, September 30, 2009
Time: 14h30
Room: Sala IAPMEI, Edificio Quelhas, ISEG
http://cemapre.iseg.ulisboa.pt/seminars/dynsys/