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Yang F, Li Y. Set-membership fuzzy filtering for nonlinear discrete-time systems. IEEE Trans Syst Man Cybern B Cybern. 2009;40(1):116-24doi: 10.1109/TSMCB.2009.2020436.
Yang, F., & Li, Y. (2010). Set-membership fuzzy filtering for nonlinear discrete-time systems. IEEE transactions on systems, man, and cybernetics. Part B, Cybernetics : a publication of the IEEE Systems, Man, and Cybernetics Society, 40(1), 116-24. https://doi.org/10.1109/TSMCB.2009.2020436
Yang, Fuwen, and Li, Yongmin. "Set-membership fuzzy filtering for nonlinear discrete-time systems." IEEE transactions on systems, man, and cybernetics. Part B, Cybernetics : a publication of the IEEE Systems, Man, and Cybernetics Society vol. 40,1 (2010): 116-24. doi: https://doi.org/10.1109/TSMCB.2009.2020436
Yang F, Li Y. Set-membership fuzzy filtering for nonlinear discrete-time systems. IEEE Trans Syst Man Cybern B Cybern. 2010 Feb;40(1):116-24. doi: 10.1109/TSMCB.2009.2020436. Epub 2009 Jul 21. PMID: 19628459.
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IEEE Trans Syst Man Cybern B Cybern. 2010 Feb;40(1):116-24. doi: 10.1109/TSMCB.2009.2020436. Epub 2009 Jul 21.

Set-membership fuzzy filtering for nonlinear discrete-time systems.

IEEE transactions on systems, man, and cybernetics. Part B, Cybernetics : a publication of the IEEE Systems, Man, and Cybernetics Society

Fuwen Yang, Yongmin Li

Affiliations

  1. School of Information Science and Engineering, East China University of Science and Technology, Shanghai 200237, China. [email protected]

PMID: 19628459 DOI: 10.1109/TSMCB.2009.2020436

Abstract

This paper is concerned with the set-membership filtering (SMF) problem for discrete-time nonlinear systems. We employ the Takagi-Sugeno (T-S) fuzzy model to approximate the nonlinear systems over the true value of state and to overcome the difficulty with the linearization over a state estimate set rather than a state estimate point in the set-membership framework. Based on the T-S fuzzy model, we develop a new nonlinear SMF estimation method by using the fuzzy modeling approach and the S-procedure technique to determine a state estimation ellipsoid that is a set of states compatible with the measurements, the unknown-but-bounded process and measurement noises, and the modeling approximation errors. A recursive algorithm is derived for computing the ellipsoid that guarantees to contain the true state. A smallest possible estimate set is recursively computed by solving the semidefinite programming problem. An illustrative example shows the effectiveness of the proposed method for a class of discrete-time nonlinear systems via fuzzy switch.

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