Observation and sliding mode observer for nonlinear fractional-order system with unknown input

Nadia Djeghali; Said Djennoune; Maamar Bettayeb; Malek Ghanes; Jean-Pierre Barbot

doi:10.1016/j.isatra.2016.02.015

Observation and sliding mode observer for nonlinear fractional-order system with unknown input

ISA Trans. 2016 Jul:63:1-10. doi: 10.1016/j.isatra.2016.02.015. Epub 2016 Mar 5.

Authors

Nadia Djeghali¹, Said Djennoune², Maamar Bettayeb³, Malek Ghanes⁴, Jean-Pierre Barbot⁵

Affiliations

¹ Laboratoire de Conception et Conduite des Systèmes de Production, University Mouloud Mammeri, Tizi-Ouzou, Algeria. Electronic address: djeghali_nadya@yahoo.fr.
² Laboratoire de Conception et Conduite des Systèmes de Production, University Mouloud Mammeri, Tizi-Ouzou, Algeria. Electronic address: s_djennoune@yahoo.fr.
³ Department of Electrical & Computer Engineering, University of Sharjah, United Arab Emirates; Distinguished Adjoint Professor at Center of Excellence in Intelligent Engineering Systems (CEIES), King Abdulaziz University, Jeddah, Saudi Arabia. Electronic address: maamar@sharjah.ac.ae.
⁴ ECS-Lab, ENSEA, 6 avenue du Ponceau, 95014 Cergy-Pontoise, France. Electronic address: Malek.Ghanes@ensea.fr.
⁵ ECS-Lab, ENSEA, 6 avenue du Ponceau, 95014 Cergy-Pontoise, France. Electronic address: barbot@ensea.fr.

PMID: 26961320
DOI: 10.1016/j.isatra.2016.02.015

Abstract

The main purpose of this paper is twofold. First, the observability and the left invertibility properties and the observable canonical form for nonlinear fractional-order systems are introduced. By using a transformation, we show that these properties can be deduced from an equivalent nonlinear integer-order system. Second, a step by step sliding mode observer for fault detection and estimation in nonlinear fractional-order systems is proposed. Starting with a chained fractional-order integrators form, a step by step first-order sliding mode observer is designed. The finite time convergence of the observer is established by using Lyapunov stability theory. A numerical example is given to illustrate the performance of the proposed approach.

Keywords: Fault detection and estimation; Left invertibility; Lyapunov stability; Nonlinear fractional-order systems; Observability; Sliding mode observers.