Optimizing the membership functions of a fuzzy system can be viewed as a system identification problem for a nonlinear dynamic system. Basically, we can view the optimization of fuzzy membership functions as a weighted least-squares minimization problem, where the error vector is the difference between the fuzzy system outputs and the target values for those outputs. The extended Kalman filter algorithm is a good choice to solve this system identification problem, not only because it is a derivative-based algorithm that is suitable to solve the weighted least-squares minimization problem, but also because of its appealing predictor-corrector feature for nonlinear system model. In this paper, we present an extended Kalman filter approach to optimize the membership functions of the inputs and outputs of the fuzzy controller. The effect of the measurement noise covariance R on the convergence of the fuzzy controller is also investigated. Experimental results show that the optimized fuzzy controller achieves significant improvement on performance. In addition, the smaller the measurement noise covariance R is, the faster the optimized fuzzy controller would converge.
N. Zhang and D. C. Wunsch, "An Extended Kalman Filter (EKF) Approach on Fuzzy System Optimization Problem," Proceedings of the 12th IEEE International Conference on Fuzzy Systems, 2003. FUZZ '03, Institute of Electrical and Electronics Engineers (IEEE), Jan 2003.
The definitive version is available at http://dx.doi.org/10.1109/FUZZ.2003.1206649
12th IEEE International Conference on Fuzzy Systems, 2003. FUZZ '03
Electrical and Computer Engineering
Keywords and Phrases
EKF; Kalman Filters; Convergence; Derivative Based Algorithm; Error Vector; Extended Kalman Filter; Fuzzy Control; Fuzzy Controller; Fuzzy Membership Functions; Fuzzy Set Theory; Fuzzy Systems; Identification; Least Squares Approximations; Minimisation; Noise Covariance; Nonlinear Control Systems; Nonlinear Dynamic Systems; Optimization; Predictor-Corrector Feature; System Identification Problem; Weighted Least Squares Minimization
Article - Conference proceedings
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