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Handbook of Optimization pp 451–479Cite as

Takagi-Sugeno Fuzzy Representation to Modelling and State Estimation

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Part of the book series: Intelligent Systems Reference Library ((ISRL,volume 38))

Abstract

This chapter shows the interest of Takagi-Sugeno (T-S) fuzzy model approach to apprehend nonlinear behaviors of physical systems and its application for observers design. From mathematical nonlinear model or experimental data, a T-S representation can be obtained using different techniques. This approach is largely exploited in many fields such as control, diagnosis and fault-tolerant control. Then the design of a robust T-S observer is addressed. The chapter considers a robust observer with respect to the uncertainties as well as unknown inputs. The synthesis of sufficient design conditions are performed using Lyapunov functions and set of linear matrix inequalities (\(\mathcal{LMI}\)). Two case studies are given. An example, dealing with a turbojet plane, shows how to obtain T-S representation using optimization algorithms. The validity of the proposed observer design is based on automatic steering of vehicles.

This work was supported by CNRS Nord-Pas de calais Picadie in the framework of the delegation (Feb 1st - Juil 31, 2012) granted to M. Chadli at LAMIH (UMR CNRS 8530).

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Author information

Authors and Affiliations

  1. Laboratory of Modeling Information & Systems, University of Picardie Jules Verne, 7, Rue du Moulin Neuf, 80000, Amiens, France

    Mohammed Chadli

  2. University of Valenciennes Le Mont Houy, Bat. Jonas 1, 59313, Valenciennes Cedex 9, France

    Thierry-Marie Guerra

  3. Department of Computer Science, Faculty of Electrical Engineering and Computer Science, VŁB-TUO, 17. listopadu 15, 708 33, Ostrava-Poruba, Czech Republic

    Ivan Zelinka

Authors
  1. Mohammed Chadli
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  2. Thierry-Marie Guerra
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  3. Ivan Zelinka
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Correspondence to Mohammed Chadli .

Editor information

Editors and Affiliations

  1. Technical University of Ostrava, 17. listopadu 15, Ostrava-Porub, 708 33, Czech Republic

    Ivan Zelinka

  2. , Faculty of Electrical Engineering and, Technical University of Ostrava, 17. listopadu 15, Ostrava-Poruba, 708 33, Czech Republic

    Václav Snášel

  3. Auburn, 98071, USA

    Ajith Abraham

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Chadli, M., Guerra, TM., Zelinka, I. (2013). Takagi-Sugeno Fuzzy Representation to Modelling and State Estimation. In: Zelinka, I., Snášel, V., Abraham, A. (eds) Handbook of Optimization. Intelligent Systems Reference Library, vol 38. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30504-7_18

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  • DOI: https://doi.org/10.1007/978-3-642-30504-7_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-30503-0

  • Online ISBN: 978-3-642-30504-7

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