scispace - formally typeset
Search or ask a question
Proceedings Article•DOI•

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

Souad Bezzaoucha1, Holger Voos1, Mohamed Darouach2•
University of Luxembourg1, University of Lorraine2
01 Jun 2016-pp 1146-1152
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 (1 min read)

Jump to:  and [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.

Did you find this useful? Give us your feedback

Content maybe subject to copyright    Report

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
References
More filters
Journal Article•DOI•
Parameterized linear matrix inequality techniques in fuzzy control system design

[...]

Hoang Duong Tuan1, Pierre Apkarian2, Tatsuo Narikiyo3, Y. Yamamoto3•
Toyota1, Community emergency response team2, Toyota Technological Institute3
01 Apr 2001-IEEE Transactions on Fuzzy Systems
TL;DR: This paper proposes different parameterized linear matrix inequality (PLMI) characterizations for fuzzy control systems and these characterizations are relaxed into pure LMI programs, which provides tractable and effective techniques for the design of suboptimal fuzzy control Systems.
Abstract: This paper proposes different parameterized linear matrix inequality (PLMI) characterizations for fuzzy control systems. These PLMI characterizations are, in turn, relaxed into pure LMI programs, which provides tractable and effective techniques for the design of suboptimal fuzzy control systems. The advantages of the proposed methods over earlier ones are then discussed and illustrated through numerical examples and simulations.

1,099 citations

"A polytopic approach for the nonlin..." refers background in this paper

  • ...The polytopic Takagi-Sugeno (T-S) or Multiple Models (MM) decomposition is another appealing alternative solution to deal with nonlinear systems and to obtain the equivalent representation by a compact set of linear state space models with nonlinear weighting functions satisfying the convex sum property [23], [24], and [28]....

    [...]

Journal Article•DOI•
Full-order observers for linear systems with unknown inputs

[...]

Mohamed Darouach, Michel Zasadzinski, S.J. Xu
01 Mar 1994-IEEE Transactions on Automatic Control
TL;DR: This note presents a simple method to design a full-order observer for linear systems with unknown inputs and the necessary and sufficient conditions for the existence of the observer are given.
Abstract: This note presents a simple method to design a full-order observer for linear systems with unknown inputs. The necessary and sufficient conditions for the existence of the observer are given. >

780 citations

"A polytopic approach for the nonlin..." refers methods in this paper

  • ...Thanks to the convexity of the weighting functions and to the linearity of the subsystems defining the vertices, some results can be established for nonlinear systems [7], [12], [17] using tools borrowed from the linear theory [18], [9]....

    [...]

Book•
Nonlinear observers and applications

[...]

Gildas Besancon
01 Aug 2007
TL;DR: This paper presents an overview of Observer Tools for Nonlinear Systems and their applications, and discusses Parameter/Fault Estimation in Nonlinear systems and Adaptive Observers.
Abstract: An Overview on Observer Tools for Nonlinear Systems.- Uniform Observability and Observer Synthesis.- Adaptive-Gain Observers and Applications.- Immersion-Based Observer Design.- Nonlinear Moving Horizon Observers: Theory and Real-Time Implementation.- Asymptotic Analysis and Observer Design in the Theory of Nonlinear Output Regulation.- Parameter/Fault Estimation in Nonlinear Systems and Adaptive Observers.

475 citations

"A polytopic approach for the nonlin..." refers methods in this paper

  • ...One solution is to transform the system model into a canonical form [3], which may be a hard assumption to satisfy in many applications [5]....

    [...]

Journal Article•DOI•
Nonlinear observer design using Lyapunov's auxiliary theorem

[...]

Nikolaos Kazantzis1, Costas Kravaris1•
University of Michigan1
27 Jul 1998-Systems & Control Letters
TL;DR: In this article, a nonlinear observer design problem is formulated via a system of singular first-order linear PDEs, and a rather general set of necessary and sufficient conditions for solvability is derived by using Lyapunov's auxiliary theorem.

398 citations

Journal Article•DOI•
Robust Observer Design for Unknown Inputs Takagi–Sugeno Models

[...]

Mohammed Chadli1, Hamid Reza Karimi2•
University of Picardie Jules Verne1, University of Agder2
01 Feb 2013-IEEE Transactions on Fuzzy Systems
TL;DR: This paper deals with the observer design for Takagi-Sugeno (T-S) fuzzy models subject to unknown inputs and disturbance affecting both states and outputs of the system.
Abstract: This paper deals with the observer design for Takagi-Sugeno (T-S) fuzzy models subject to unknown inputs and disturbance affecting both states and outputs of the system. Sufficient conditions to design an unknown input T-S observer are given in linear matrix inequality (LMI) terms. Both continuous-time and discrete-time cases are studied. Relaxations are introduced by using intermediate variables. Extension to the case of unmeasured decision variables is also given. A numerical example is given to illustrate the effectiveness of the given results.

384 citations

"A polytopic approach for the nonlin..." refers background in this paper

  • ...) acts like an unstructured vanishing perturbation assumed to be bounded (see [ [2]], [ [6]] and references therein) and its effect can be minimized....

    [...]

Related Papers (5)
Nonlinear Flight Control Strategy for an Underactuated Quadrotor Aerial Robot

[...]

06 Apr 2008
A.A. Mian, Wang Daobo
Adaptive Backstepping Tracking Control for Quadrotor Aerial Robots Subject to Uncertain Dynamics

[...]

10 Jul 2019
Ou Tsung-Wei, Yen-Chen Liu
Lyapunov-based nonlinear controller for quadrotor position and attitude tracking with GA optimization

[...]

01 Nov 2016
Ali Safaei, Muhammad Nasiruddin Mahyuddin
Robust tracking control of an underactuated quadrotor aerial-robot based on a parametric uncertain model

[...]

11 Oct 2009
DongBin Lee, Timothy C. Burg, Darren M. Dawson, Dule Shu, Bin Xian, Enver Tatlicioglu 
The Trajectory Tracking Problem of Quadrotor UAV: Global Stability Analysis and Control Design Based on the Cascade Theory

[...]

01 Mar 2014-Asian Journal of Control
Lu Wang, Heming Jia