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Finding the golden mean in data-driven modeling

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

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Finding the golden mean in data-driven modeling

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  1. Finding the golden mean in data-driven modeling

  2. An observation • Real World Systems • LTI Modeling • LTI Control Theory • 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 We have already reached the limitations of the LTI framework due to the increasing performance demands

  3. An observation (cont’d) How to find the golden mean between simplicity and accuracy? Can we embed or approximate NL/TV behaviors with linear structures? LTI system identification Vast universe of Nonlinear and Time-Varying systems LPV PWA LTV SL

  4. LPV models The concept

  5. Challenges • Focus: • How to select which model class (PWA, LPV, etc.) to use based on data? (better understanding the represented behaviors) • Structure exploration:learningthe 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 ...

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