Representing and Computing the B-Derivative of the Piecewise-Differentiable Flow of a Class of Nonsmooth Vector Fields
Abstract
This paper concerns first-order approximation of the piecewise-differentiable flow generated by a class of nonsmooth vector fields. Specifically, we represent and compute the Bouligand (or B-)derivative of the piecewise-differentiable flow generated by a vector field with event-selected discontinuities. Our results are remarkably efficient: although there are factorially many “pieces” of the derivative, we provide an algorithm that evaluates its action on a tangent vector using polynomial time and space, and verify the algorithm's correctness by deriving a representation for the B-derivative that requires “only” exponential time and space to construct. We apply our methods in two classes of illustrative examples: piecewise-constant vector fields and mechanical systems subject to unilateral constraints.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Jun 03, 2022
- Source ID
- 10.1115/1.4054481
Entities
People
- George Council
- Samuel A. Burden
- Shai Revzen
Organizations
- Army Research Office
- Carnegie Mellon University
- Division of Electrical, Communications & Cyber Systems
- University of Michigan
- University of Washington