Observability of nonlinear dynamics: normalized results and a time-series approach

Luis A Aguirre; Saulo B Bastos; Marcela A Alves; Christophe Letellier

doi:10.1063/1.2885386

Observability of nonlinear dynamics: normalized results and a time-series approach

Chaos. 2008 Mar;18(1):013123. doi: 10.1063/1.2885386.

Authors

Luis A Aguirre¹, Saulo B Bastos, Marcela A Alves, Christophe Letellier

Affiliation

¹ Programa de Pós-graduação em Engenharia Elétrica, Universidade Federeal de Minas Gerais, 31270-901 Belo Horizonte, MG, Brazil.

PMID: 18377074
DOI: 10.1063/1.2885386

Abstract

This paper investigates the observability of nonlinear dynamical systems. Two difficulties associated with previous studies are dealt with. First, a normalized degree observability is defined. This permits the comparison of different systems, which was not generally possible before. Second, a time-series approach is proposed based on omnidirectional nonlinear correlation functions to rank a set of time series of a system in terms of their potential use to reconstruct the original dynamics without requiring the knowledge of the system equations. The two approaches proposed in this paper and a former method were applied to five benchmark systems and an overall agreement of over 92% was found.