A polytopic approach for the nonlinear unknown input functional observers design: Application to a quadrotor aerial robots landing

TL;DR: The proposed approach consists in rewriting the nonlinear model in a polytopic form applying the Sector Non-linearity Transformation (SNT) and then applying the proposed algorithm for the observer design.

Abstract: This paper considers a method of designing functional observers for continuous time nonlinear systems subject to unknown inputs. The proposed approach consists in rewriting the nonlinear model in a polytopic form (also known as multiple or Takagi-Sugeno models) applying the Sector Non-linearity Transformation (SNT) and then apply the proposed algorithm for the observer design. Sufficient conditions for the asymptotic stability of the estimation error are given in terms of linear matrix inequalities (LMls) and rank conditions. An application to a quadrotor aerial robots landing is then presented.

Summary

Summary

• This paper considers a method of designing functional observers for continuous time nonlinear systems subject to unknown inputs.
• The proposed approach consists in rewriting the nonlinear model in a polytopic form (also known as multiple or Takagi-Sugeno models) applying the Sector Nonlinearity Transformation (SNT) and then apply the proposed algorithm for the observer design.
• Sufficient conditions for the asymptotic stability of the estimation error are given in terms of linear matrix inequalities (LMIs) and rank conditions.

Full text

A Polytopic Approach for the Nonlinear Unknown Input Functional
Observers Design: Application to a Quadrotor Aerial Robots Landing
Souad Bezzaoucha
1
, Holger Voos
1
and Mohamed Darouach
2
Abstract— This paper considers a method of designing func-
tional observers for continuous time nonlinear systems subject
to unknown inputs. The proposed approach consists in re-
writing the nonlinear model in a polytopic form (also known
as multiple or Takagi-Sugeno models) applying the Sector Non-
linearity Transformation (SNT) and then apply the proposed
algorithm for the observer design. Sufficient conditions for the
asymptotic stability of the estimation error are given in terms
of linear matrix inequalities (LMIs) and rank conditions.
An application to a quadrotor aerial robots landing is then
presented.
1
Souad Bezzaoucha and Holger Voos are with the Interdisciplinary
Centre for Security, Reliability and Trust (SnT), Automatic Control
Research Group, University of Luxembourg, Campus Kirchberg, 6
rue Coudenhove-Kalergi L-1359, Luxembourg souad.bezzaoucha,
holger.voos@uni.lu
2
Mohamed Darouach is with the Research Center for Auto-
matic Control of Nancy (CRAN), Universit
´
e de Lorraine, IUT de
Longwy, 186 rue de Lorraine, 54400 Cosnes et Romain, France
mohamed.darouach@univ-lorraine.fr