Title: Information extraction from reduced order models using Shannon entropy-based approach

Date/Time: Wednesday, June 7, 2006, 10:00-11:00 am

Location: Building 980, Room 95 (Sandia NM)

Brief Abstract: In projection-based model reduction method (e.g. Balanced Truncation, Krylov subspace, proper orthogonal decomposition), the reduced basis which approximates the original dynamics represents the system's main dynamical features.  Depending on the applied methods, the dynamical features are derived from the collected state variable evolutions, controllability, or observability Gramians. The original physical interpretations of the original variables are generally lost in the reduced model. The original variables are entangled in the reduced basis.

The entanglement leads to the problem of identifying the relations between the original and reduced state variables. These relations are needed for example in control system design. It is a common practice to replace the high order model by a reduced model in model-based control as controllers are unable to handle high order models. On the other hand, the original control problem is usually posed as a function of original state variables. For instance, we would like to control the temperature in a particular spot and the control weighting should be very large in that spot. If we use a reduced order model, how do we assign a proper weighting to the reduced state variables? In engineering system design, how do we use the reduced models to investigate the influence of some original variables in the overal dynamics?

This presentation presents an empirical method developed from the Shannon Entropy concept in order to identify the relations between the original and reduced state variables. The empirical relations are applied in the closed loop control design of a spatio-temporal model reduced by the POD method. The incorporation of the empirical relations in the closed loop design results in a more effective closed loop performance.

CSRI POC: Bart van Bloemen Waanders, (505) 284-6746