General Inner Approximation of Vector-valued Functions

Olivier Mullier (1) , Eric Goubault (2) , Michel Kieffer (3, 4) , Sylvie Putot (2)

1 LMeASI - Laboratoire Modélisation et Analyse de Systèmes en Interaction
2 LIST (CEA) - Laboratoire d'Intégration des Systèmes et des Technologies
3 L2S - Laboratoire des signaux et systèmes
4 LTCI - Laboratoire Traitement et Communication de l'Information

This paper addresses the problem of evaluating a subset of the range of a vector-valued function. It is based on a work by Goldsztejn and Jaulin which provides methods based on interval analysis to address this problem when the dimension of the domain and co-domain of the function are equal. This paper extends this result to vector-valued functions with domain and co-domain of different dimensions. This extension requires the knowledge of the rank of the Jacobian function on the whole domain. This leads to the sub-problem of extracting an interval sub-matrix of maximum rank from a given interval matrix. Three different techniques leading to approximate solutions of this extraction are proposed and compared.

Domains: Automatic Control Engineering

Olivier Mullier, Eric Goubault, Michel Kieffer, Sylvie Putot. General Inner Approximation of Vector-valued Functions. Reliable Computing, 2013, 18, pp.117-143. ⟨hal-00935773⟩