Fuzzy Set-Membership Filtering for Discrete-Time Nonlinear Systems

• Published in: IEEE/CAA journal of automatica sinica Vol. 9; no. 6; pp. 1026 - 1036
• Main Authors: Mao, Jingyang, Meng, Xiangyu, Ding, Derui
• Format: Journal Article
• Language: English
• Published: Piscataway Chinese Association of Automation (CAA) 01.06.2022; The Institute of Electrical and Electronics Engineers, Inc. (IEEE); Department of Control Science and Engineering,University of Shanghai for Science and Technology,Shanghai 200093,China%Division of Electrical and Computer Engineering,Louisiana State University,Baton Rouge,LA,70803 USA %Department of Control Science and Engineering,University of Shanghai for Science and Technology,Shanghai 200093,China; School of Science,Computing and Engineering Technologies,Swinburne University of Technology,Melbourne,VIC 3122,Australia
• Subjects: Affine model; Algorithms; Continuity (mathematics); Discrete time systems; Ellipsoids; Estimation error; Filtering algorithms; Filtering theory; Filtration; Fuzzy sets; Information filters; Mathematical analysis; Mathematical models; membership functions; Noise measurement; Nonlinear systems; Optimization; set-membership filtering; stability; State estimation; Takagi-Sugeno fuzzy modeling; membership functions; Affine model; Takagi-Sugeno fuzzy modeling; stability; set-membership filtering
• ISSN: 2329-9266; 2329-9274
• DOI: 10.1109/JAS.2022.105416

In this article, the problem of state estimation is addressed for discrete-time nonlinear systems subject to additive unknown-but-bounded noises by using fuzzy set-membership filtering. First, an improved T-S fuzzy model is introduced to achieve highly accurate approximation via an affine model under each fuzzy rule. Then, compared to traditional prediction-based ones, two types of fuzzy set-membership filters are proposed to effectively improve filtering performance, where the structure of both filters consists of two parts: prediction and filtering. Under the locally Lipschitz continuous condition of membership functions, unknown membership values in the estimation error system can be treated as multiplicative noises with respect to the estimation error. Real-time recursive algorithms are given to find the minimal ellipsoid containing the true state. Finally, the proposed optimization approaches are validated via numerical simulations of a one-dimensional and a three-dimensional discrete-time nonlinear systems.