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Proceedings ArticleDOI

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

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.

AbstractThis 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.

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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.

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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
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Abstract: A mathematical tool to build a fuzzy model of a system where fuzzy implications and reasoning are used is presented. The premise of an implication is the description of fuzzy subspace of inputs and its consequence is a linear input-output relation. The method of identification of a system using its input-output data is then shown. Two applications of the method to industrial processes are also discussed: a water cleaning process and a converter in a steel-making process.

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

  • ...Originally introduced by [22], the T-S representation allows to exactly describe nonlinear systems, under the condition that the nonlinearities are bounded....

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TL;DR: Fuzzy Control Systems Design and Analysis offers an advanced treatment of fuzzy control that makes a useful reference for researchers and a reliable text for advanced graduate students in the field.
Abstract: From the Publisher: A comprehensive treatment of model-based fuzzy control systems This volume offers full coverage of the systematic framework for the stability and design of nonlinear fuzzy control systems. Building on the Takagi-Sugeno fuzzy model, authors Tanaka and Wang address a number of important issues in fuzzy control systems, including stability analysis, systematic design procedures, incorporation of performance specifications, numerical implementations, and practical applications. Issues that have not been fully treated in existing texts, such as stability analysis, systematic design, and performance analysis, are crucial to the validity and applicability of fuzzy control methodology. Fuzzy Control Systems Design and Analysis addresses these issues in the framework of parallel distributed compensation, a controller structure devised in accordance with the fuzzy model. This balanced treatment features an overview of fuzzy control, modeling, and stability analysis, as well as a section on the use of linear matrix inequalities (LMI) as an approach to fuzzy design and control. It also covers advanced topics in model-based fuzzy control systems, including modeling and control of chaotic systems. Later sections offer practical examples in the form of detailed theoretical and experimental studies of fuzzy control in robotic systems and a discussion of future directions in the field. Fuzzy Control Systems Design and Analysis offers an advanced treatment of fuzzy control that makes a useful reference for researchers and a reliable text for advanced graduate students in the field.

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  • ...Proof: To prove this lemma, we need the following results: Lemma 4: [23] The continuous polytopic system  ẋ(t) = M ∑...

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