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Balancing Simplicity and Accuracy in Data-Driven Modeling of Nonlinear and Time-Varying Systems

As the demands for performance increase, the limitations of Linear Time-Invariant (LTI) frameworks become evident. This observation highlights the need to find a "golden mean" between simplicity and accuracy in modeling real-world systems. By exploring various model classes—such as Piecewise Affine (PWA) and Linear Parameter-Varying (LPV)—we can better understand and identify nonlinear (NL) and time-varying (TV) behaviors through efficient structure exploration. Collaborating with fields like machine learning can enhance model selection, enabling us to develop more robust control strategies while minimizing assumptions.

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Balancing Simplicity and Accuracy in Data-Driven Modeling of Nonlinear and Time-Varying Systems

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Presentation Transcript

  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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