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Avoiding Matrix Inversion in Takagi–Sugeno-Based Advanced Controllers and Observers

Abstract : Many of the recent advances on control and estimation of systems described by Takagi-Sugeno (TS) fuzzy models are based on matrix inversion, which could be a trouble in the case of real-time implementation. This paper is devoted to the development of alternative solutions to this matrix inversion problem in the discrete-time case. Two different methods are proposed: The first one relies on replacing the matrix inversion by multiple sums and the second methodology is based on an estimation of the matrix inversion by an observer structure. For the first methodology, a new class of controllers and observers are introduced which are called, respectively, the counterpart of an advanced TS-based (CATS) controller and the replica of an advanced TS-based (RATS) observer. Instead of relaxations for the linear matrix inequalities conditions, an original use of the membership functions is presented. In the second methodology, it is proposed the estimation-based control law for approximating TS-based (ECLATS) controller that uses a fuzzy state observer. The Lyapunov theory is used to ensure stability conditions for either the closed-loop system as well as the estimation error. Numerical examples and comparisons highlight the efficiency of the procedures that can be used to replace any inverted matrix in any advanced fuzzy controller or observer. Finally, advantages and drawbacks of the proposed method are discussed.
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Submitted on : Monday, November 15, 2021 - 9:35:24 AM
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Thomas Laurain, Jimmy Lauber, Reinaldo Martinez Palhares. Avoiding Matrix Inversion in Takagi–Sugeno-Based Advanced Controllers and Observers. IEEE Transactions on Fuzzy Systems, Institute of Electrical and Electronics Engineers, 2018, 26 (1), pp.216-225. ⟨10.1109/TFUZZ.2017.2647992⟩. ⟨hal-03428201⟩



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