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.
PDF@inproceedings{Jin2022,
title = {Learning Linear Complementarity Systems},
author = {Jin, Wanxin and Aydinoglu, Alp and Halm, Mathew and Posa, Michael},
booktitle = {Proceedings of The 4th Annual Learning for Dynamics and Control Conference (L4DC)},
pages = {1137--1149},
year = {2022},
editor = {Firoozi, Roya and Mehr, Negar and Yel, Esen and Antonova, Rika and Bohg, Jeannette and Schwager, Mac and Kochenderfer, Mykel},
volume = {168},
series = {Proceedings of Machine Learning Research},
month = {23--24 Jun},
publisher = {PMLR},
pdf = {https://proceedings.mlr.press/v168/jin22a/jin22a.pdf},
url = {https://proceedings.mlr.press/v168/jin22a.html},
arxiv = {2112.13284},
code = {https://github.com/DAIRLab/Learning-LCS}
}