Set-membership fuzzy filtering for nonlinear discrete-time systems

  • Authors:

  • Fuwen Yang;Yongmin Li

  • Affiliations:

  • School of Information Science and Engineering, East China University of Science and Technology, Shanghai, China and Department of Information Systems and Computing, Brunel University, Middlesex, U ...;Department of Information Systems and Computing, Brunel University, Middlesex, UK

  • Venue:
  • IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
  • Year:
  • 2010

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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.