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 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 the clustering-based piecewise-affine regression methods and the methods which must differentiate through non-smooth linear complementarity constraints.

In Conference on Learning for Dynamics and Control
Alp Aydınoğlu
Alp Aydınoğlu
PhD Student in GRASP Lab

My research interests include optimization, control theory, learning and mechanics (particularly non-smooth mechanics).