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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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
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