Learning Linear Complementarity Systems

This paper investigates the learning, or system identification, of a class of piecewise-affine dynamical systems known as linear complementarity systems (LCSs). We propose a violation-based loss which enables efficient learning of the LCS parameterization, without prior knowledge of the hybrid mode...

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Bibliographic Details
Published inarXiv.org
Main Authors Jin, Wanxin, Aydinoglu, Alp, Halm, Mathew, Posa, Michael
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 25.12.2021
Subjects
Dynamical systems
Hybrid modes
Learning
Parameterization
System identification
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Summary:This paper investigates the learning, or system identification, of a class of piecewise-affine dynamical systems known as linear complementarity systems (LCSs). We propose a violation-based loss which enables efficient learning of the LCS parameterization, without prior knowledge of the hybrid mode boundaries, using gradient-based methods. The proposed violation-based loss incorporates both dynamics prediction loss and a novel complementarity - violation loss. We show several properties attained by this loss formulation, including its differentiability, the efficient computation of first- and second-order derivatives, and its relationship to the traditional prediction loss, which strictly enforces complementarity. We apply this violation-based loss formulation to learn LCSs with tens of thousands of (potentially stiff) hybrid modes. The results demonstrate a state-of-the-art ability to identify piecewise-affine dynamics, outperforming methods which must differentiate through non-smooth linear complementarity problems.
ISSN:2331-8422