finding the golden mean in data-driven modeling
DESCRIPTION
Finding the golden mean in data-driven modeling. An observation. Real World Systems. LTI Modeling. LTI Control Theory. D ynamical systems in engineering Nonlinear behavior ( NL-ODE’s , DAE’s ) Time-varying behavior Spatial components ( PDE’s ) Classical concept of digital control - PowerPoint PPT PresentationTRANSCRIPT
July 13, 2012, Brussels
Challenge the future
DelftUniversity ofTechnology
Delft Center for Systems and Control
R. Tóth
Finding the golden mean in data-driven modeling
2
Challenge the future
DelftUniversity ofTechnology
Delft Center for Systems and Control
• Dynamical systems in engineering• Nonlinear behavior (NL-ODE’s,
DAE’s)
• Time-varying behavior
• Spatial components (PDE’s)
• Classical concept of digital control• Linear Time-Invariant (LTI)
framework
• Linearization principle
An observation
LTI Control Theory
LTI Modelin
g
Real World
Systems
We have already reached the limitations of the LTI framework due to the increasing performance
demands
3
Challenge the future
DelftUniversity ofTechnology
Delft Center for Systems and Control
An observation (cont’d)
LTI system identification
Vast universe of Nonlinear and Time-
Varying systems
How to find the golden mean
between simplicity and accuracy?
Can we embed or approximate NL/TV
behaviors with linear structures?
LTV
LPV PWA
SL
4
Challenge the future
DelftUniversity ofTechnology
Delft Center for Systems and Control
LPV modelsThe concept
5
Challenge the future
DelftUniversity ofTechnology
Delft Center for Systems and Control
• Focus:
• How to select which model class (PWA, LPV, etc.) to use based on data? (better understanding the represented behaviors)
• Structure exploration: learning the manifesting functional dependencies, model order etc. is extremely important (efficient embedding of the behavior) [Co-op with other communities like machine learning and evolutionary algorithms]
• Use less assumptions, but try to use as many priors. Attach “uncertainty certificate” to priors.
• Identification of controllers ...
Challenges