Data-Driven Abstraction and Model Invalidation for Unknown Systems With Bounded Jacobians

Zeyuan Jin, Mohammad Khajenejad, Sze Zheng Yong

Research output: Contribution to journalArticlepeer-review

Abstract

In this letter, we consider data-driven abstraction and model invalidation problems for unknown nonlinear discrete-time dynamical systems with bounded Jacobians, where only prior noisy sampled data of the systems, instead of mathematical models, are available. First, we introduce a novel non-parametric learning approach to over-approximate the unknown model/dynamics with upper and lower functions, i.e., to find model abstractions, under the assumption of known bounded Jacobians. Notably, the resulting data-driven models can be mathematically proven to be equal to or more accurate than componentwise Lipschitz continuity-based methods. Further, we show that the resulting data-driven model can be used to determine its (in)compatibility with a newly observed length-$T$ output trajectory, i.e., to (in)validate models, using a tractable feasible check. Finally, we propose a method to estimate the Jacobian bounds if they are not known or given.

Original languageEnglish (US)
Pages (from-to)3421-3426
Number of pages6
JournalIEEE Control Systems Letters
Volume6
DOIs
StatePublished - 2022

Keywords

  • Model validation
  • Nonlinear systems identification

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Control and Optimization

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