This article presents an efficient TSK-type recurrent fuzzy cerebellar model articulation controller (T-RFCMAC) model based on a dynamic-group-based hybrid evolutionary algorithm (DGHEA) for solving identification and prediction problems. The proposed T-RFCMAC model is based on the traditional CMAC model and the Takagi-Sugeno-Kang (TSK) parametric fuzzy inference system. Otherwise, the recurrent network, which imports feedback links with a receptive field cell, is embedded in the T-RFCMAC model, and the feedback units are used as memory elements. The DGHEA, which is a hybrid of the dynamic-group quantum particle swarm optimization (QPSO) and the Nelder-Mead method, is proposed for adjusting the parameters of the T-RFCMAC model. In DGHEA, an entropybased grouping technique is adopted to improve the searching capability and the convergent speed of quantum particles swarm optimization. Experimental results show that the proposed DGHEA-based T-RFCMAC model is more effective at identification and prediction than other models.
IntroductionFor nonlinear system processing, neural networks or neural fuzzy networks [1][2][3] are the most commonly used model. If a feedforward network is applied in the dynamic system, we first need to obtain the delay numbers of outputs and inputs [3]. In this situation, the accurate order of the dynamic system is usually not clear. To solve this problem, recurrent networks [4,5] are adopted for processing the dynamic system. In the present study, we present a novel recurrent network for solving different problems.The cerebellar model articulation controller (CMAC) model was proposed by Albus [6,7]. It is a simple network architecture with a high convergence rate, high learning speed, good generalization capability, ease of hardware implementation, etc. The CMAC network has been employed in various areas successfully, such as robot control [8], pattern recognition [9], and signal processing [10]. However, Albus's CMAC network still has three major limitations. First, it is difficult to select the memory structure parameters. While the common CMAC network has a constant value allocated to each hypercube, the derivative information is not maintained and the data for a quantized state are constant. In order to solve this problem, inconstant differentiable basis functions are used, such as fuzzy membership functions by Jou [11] and spline functions by Lane et al.