Discrete-time Kalman filter for Takagi–Sugeno fuzzy models

In this work, the Kalman Filter (KF) and Takagi–Sugeno fuzzy modeling technique are combined to extend the classical Kalman linear state estimation to the nonlinear field. The framework for such extension is given, and in this sense the discrete-time fuzzy Kalman filter (DFKF) is obtained. It will be shown that the fuzzy version gives some advantages when is compared with the Extended Kalman Filter (EKF), which is the most typical extension of the KF to the nonlinear field. The proposed approach provides a significantly smaller processing time than the processing time of the EKF while the mean square error is also reduced. Finally, some examples, such as the Lorenz chaotic attractor and under actuated mechatronic system (pendubot), are used to compare the DFKF and EKF.

[1]  Mahardhika Pratama,et al.  Scaffolding type-2 classifier for incremental learning under concept drifts , 2016, Neurocomputing.

[2]  Payman Moallem,et al.  Fuzzy Inference System Optimized by Genetic Algorithm for Robust Face and Pose Detection , 2015 .

[3]  Lazaros S. Iliadis,et al.  Timely advances in evolving neural-based systems special issue , 2016, Evol. Syst..

[4]  José de Jesús Rubio,et al.  Least square neural network model of the crude oil blending process , 2016, Neural Networks.

[5]  Bala Srinivasan,et al.  AnyNovel: detection of novel concepts in evolving data streams , 2016, Evolving Systems.

[6]  Mohinder S. Grewal,et al.  Kalman Filtering: Theory and Practice Using MATLAB , 2001 .

[7]  Didier Dubois,et al.  Fuzzy sets and fuzzy information-granulation theory: key selected papers by Lotfi A. Zadeh , 2003 .

[8]  José Jesús Rubio.  Adaptive least square control in discrete time of robotic arms , 2015 .

[9]  Khaled Ghédira,et al.  Discussion and review on evolving data streams and concept drift adapting , 2018, Evol. Syst..

[10]  Kazuo Tanaka,et al.  Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach , 2008 .

[11]  Mahardhika Pratama,et al.  A novel online multi-label classifier for high-speed streaming data applications , 2016, Evolving Systems.

[12]  Fernando Gomide,et al.  Evolving granular analytics for interval time series forecasting , 2016, Granular Computing.

[13]  Chee Peng Lim,et al.  An incremental meta-cognitive-based scaffolding fuzzy neural network , 2016, Neurocomputing.

[14]  Guanrong Chen,et al.  Kalman Filtering with Real-time Applications , 1987 .

[15]  Plamen P. Angelov,et al.  A new type of simplified fuzzy rule-based system , 2012, Int. J. Gen. Syst..

[16]  T. Başar,et al.  A New Approach to Linear Filtering and Prediction Problems , 2001 .

[17]  Wen Yu,et al.  Nonlinear system identification with recurrent neural networks and dead-zone Kalman filter algorithm , 2007, Neurocomputing.

[18]  Plamen Angelov,et al.  Autonomously evolving classifier TEDAClass , 2016, Inf. Sci..

[19]  Guanrong Chen,et al.  Synchronization of chaotic systems from a fuzzy regulation approach , 2009, Fuzzy Sets Syst..

[20]  Claudia-Adina Dragos,et al.  Iterative performance improvement of fuzzy control systems for three tank systems , 2012, Expert Syst. Appl..

[21]  Wanqing Song,et al.  DIFFERENCE EQUATION OF LORENZ SYSTEM , 2013 .

[22]  Ian Petersen,et al.  A discrete-time robust extended Kalman filter , 2009, 2009 American Control Conference.

[23]  B. Castillo-Toledo,et al.  The fuzzy discrete-time robust regulation problem: a LMI approach , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[24]  Walmir M. Caminhas,et al.  A fast learning algorithm for evolving neo-fuzzy neuron , 2014, Appl. Soft Comput..

[25]  Jesús A. Meda-Campaña,et al.  Analysis of the Fuzzy Controllability Property and Stabilization for a Class of T–S Fuzzy Models , 2015, IEEE Transactions on Fuzzy Systems.

[26]  Gabriel A. Terejanu,et al.  Extended Kalman Filter Tutorial , 2009 .