An Extended Kalman Filter (EKF) Approach on Fuzzy System Optimization Problem
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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.