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  • 1.
    Bergsten, Pontus
    Örebro University, Department of Technology.
    Observers and controllers for Takagi-Sugeno fuzzy systems2001Doctoral thesis, monograph (Other academic)
    Abstract [en]

    This thesis studies analysis and design issues for observers anc controllers for Takagi-Sugeno (TS) fuzzy systems. Many physical systems are nonlinear in nature and using the well known linear techniques for such systems may result in bad performance, and even instability. On the other hand, analysis and design of observers and controllers for general nonlinear systems tend to be a quite involved procedure. It turns out, however, that a TS fuzzy system is able to represent or approximate a large class of nonlinear systems. Developing methods for observation and control for TS systems should therefore be worthwile.

    The TS fuzzy systems considered in this thesis are allowed to have an affine term. This can be an advantage, because affine TS fuzzy systems may be able to approximate nonlinear functions  to high accuracy with fewer rules than the TS fuzzy system with linear consequents only.

    It is shown that observer design is more difficult when the weights in the TS fuzzy systems depend on the estimated state, and an explicit design procedure is devised for that case. A reduced order observer is also proposed. To deal with modeling errors a fuzzy sliding mode approach is taken.

    The controller design is focused on affine TS fuzzy systems. Analysis and design of observer-based error state feedback controllers are proposed. Furthermore, it is also shown how recent results on classical gain scheduling may be used for control of affine TS fuzzy systems.

    Analysis and design for both observers and controllers are based on quadratic stability analysis, and in some cases, on robust quadratic stability analysis. Although this approach may be conservative, it often results in automatic design procedures based on optimization subject to linear matrix inequalities.

  • 2.
    Bergsten, Pontus
    et al.
    Örebro University, Department of Technology.
    Palm, Rainer
    Siemens AG Corporate Technology, Munich, Germany.
    Driankov, Dimiter
    Örebro University, Department of Technology.
    Fuzzy Observers2001In: The 10th IEEE International Conference on Fuzzy Systems (Volym:3): Meeting the grand challenge: Machines that serve people, New York, USA: IEEE conference proceedings, 2001, p. 700-703Conference paper (Refereed)
    Abstract [en]

    We consider the analysis and design of three different types of nonlinear observers for dynamic Takagi-Sugeno fuzzy systems. Our approach is based on extending existing nonlinear observer schemes, namely Thau-Luenberger and sliding mode observers, to the case of interpolated multiple local affine linear models. Then linear matrix inequality based techniques are used for observer analysis and design.

  • 3.
    Bergsten, Pontus
    et al.
    Örebro University, School of Science and Technology.
    Palm, Rainer
    Siemens AG Corporate Technology, Otto-Hahn-Ring, Munich, German.
    Driankov, Dimiter
    Örebro University, School of Science and Technology.
    Observers for Takagi-Sugeno fuzzy systems2002In: IEEE transactions on systems, man and cybernetics. Part B. Cybernetics, ISSN 1083-4419, E-ISSN 1941-0492, ISSN 1083-4419/02, Vol. 32, no 1, p. 114-121Article in journal (Refereed)
    Abstract [en]

    We focus on the analysis and design of two different sliding mode observers for dynamic Takagi-Sugeno (TS) fuzzy systems. A nonlinear system of this class is composed of multiple affine local linear models that are smoothly interpolated by weighting functions resulting from a fuzzy partitioning of the state space of a given nonlinear system subject to observation. The Takagi-Sugeno fuzzy system is then an accurate approximation of the original nonlinear system. Our approach to the analysis and design of observers for Takagi-Sugeno fuzzy systems is based on extending sliding mode observer schemes to the case of interpolated multiple local affine linear models. Thus, our main contribution is nonlinear observer analysis and design methods that can effectively deal with model/plant mismatches. Furthermore, we consider the difficult case when the weighting functions in the Takagi-Sugeno fuzzy system depend on the estimated state

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