Non-linear estimation is easy

Michel Fliess (1) , Cédric Join (1, 2) , Hebertt Sira-Ramirez (3)

1 ALIEN - Algebra for Digital Identification and Estimation
2 CRAN - Centre de Recherche en Automatique de Nancy
3 CINVESTAV - Centro de Investigacion y de Estudios Avanzados del Instituto Politécnico Nacional

Non-linear state estimation and some related topics, like parametric estimation, fault diagnosis, and perturbation attenuation, are tackled here via a new methodology in numerical differentiation. The corresponding basic system theoretic definitions and properties are presented within the framework of differential algebra, which permits to handle system variables and their derivatives of any order. Several academic examples and their computer simulations, with on-line estimations, are illustrating our viewpoint.

Keywords: Non-linear systems; observability; parametric identifiability; closed-loop state estimation; closed-loop parametric identification; closed-loop fault diagnosis; closed-loop fault tolerant control; closed-loop perturbation attenuation; numerical differentiation; differential algebra.; differential algebra

Domains: Automatic Control Engineering; Computational Engineering, Finance, and Science [cs.CE]; Performance [cs.PF]; Commutative Algebra [math.AC]; Numerical Analysis [math.NA]; Optimization and Control [math.OC]

Michel Fliess, Cédric Join, Hebertt Sira-Ramirez. Non-linear estimation is easy. International Journal of Modelling, Identification and Control, 2008, Special Issue on Non-Linear Observers, 4 (1), pp.12-27. ⟨10.1504/IJMIC.2008.020996⟩. ⟨inria-00158855v2⟩