A sufficient condition to design unknown input observers for nonlinear systems with arbitrary relative degree

Pedro Coutinho (1) , Iury Bessa (2, 3) , Wen‐bo Xie , Tran Anh-Tu Nguyen (4, 5, 6) , Reinaldo Martínez Palhares (2)

1 AFMB - Architecture et fonction des macromolécules biologiques
2 UFMG - Universidade Federal de Minas Gerais = Federal University of Minas Gerais [Belo Horizonte, Brazil]
3 Federal University of Amazonas
4 LAMIH - Laboratoire d'Automatique, de Mécanique et d'Informatique industrielles et Humaines - UMR 8201
5 INSA Hauts-De-France - INSA Institut National des Sciences Appliquées Hauts-de-France
6 UPHF - Université Polytechnique Hauts-de-France

Abstract This article addresses the problem of state and unknown inputs (UIs) estimation for nonlinear systems with arbitrary relative degree with respect to the UIs. For this purpose, a novel nonlinear unknown input observer (UIO) is proposed, which is able to decouple the UIs by using the derivatives of the output signal. The error dynamics is attained by an exact handling and a factorization of its gradient to obtain a local polytopic representation suitable for input‐affine nonlinear systems. For that representation, a novel design condition based on convex optimization and linear matrix inequalities is proposed to exponentially stabilize the estimation error and to guarantee the validity of the proposed nonlinear UIO. Numerical simulations indicate the effectiveness of the proposed approach for different classes of nonlinear systems, for which the UIs could be totally decoupled from the state estimation.

Domaines: Automatique

Pedro Coutinho, Iury Bessa, Wen‐bo Xie, Tran Anh-Tu Nguyen, Reinaldo Martínez Palhares. A sufficient condition to design unknown input observers for nonlinear systems with arbitrary relative degree. International Journal of Robust and Nonlinear Control, 2022, 32 (15), pp.8331-8348. ⟨10.1002/rnc.6273⟩. ⟨hal-04278845⟩