Learning Linear Complementarity Systems
This work addresses system identification for hybrid dynamical systems, which is incremental as it improves upon existing methods by avoiding differentiation through non-smooth problems.
The paper tackles the problem of learning linear complementarity systems (LCSs), a class of piecewise-affine dynamical systems, by proposing a violation-based loss that enables efficient gradient-based learning without prior knowledge of hybrid mode boundaries, achieving state-of-the-art performance in identifying such dynamics with tens of thousands of modes.
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.