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