Ellipsoidal arithmetic for multivariate systems

Authors

• M.E. Villanueva, J. Rajyaguru, B. Houska, B. Chachuat

Reference

• Computer Aided Chemical Engineering
  Volume 37, pages 767 - 772, 2015.

Abstract

The ability to determine enclosures for the image set of nonlinear functions is pivotal to many applications in engineering. This paper presents a method for the systematic construction of ellipsoidal extensions of factorable functions. It proceeds by lifting the ellipsoid to a higher dimensional space for every atom operation in the function DAG, thereby accounting for dependencies. We present theoretical results regarding the quadratic Hausdorff convergence of the computed enclosures. Moreover, we propose an efficient implementation, whereby the shape matrix of the lifted ellipsoid is stored in sparse format, and every atom operation corresponds to a sparse update in that matrix. We illustrate these developments with two numerical examples.

Download

• Paper

Bibtex