Macro_Structure_CMAC (MS_CMAC) is a variational CMAC neural network that is designed for modeling smooth functional mappings. The MS_CMAC learning strategy involves constructing virtual grid-distributed data points from random-distributed training data points, and then using the virtual data points to train a tree structure network that is composed of one-dimensional CMAC nodes. A disadvantage of the MS_CMAC is that the prediction errors near the boundary area might sometimes be unexpectedly large. Another disadvantage of the MS_CMAC is that generating virtual grid-distributed data points generally takes a long computational time. Therefore, this study develops an improved model by integrating an unsupervised fuzzy neural network (UFN) into the MS_CMAC to initialize systematically the virtual grid-distributed data points. Additionally, a new error feedback ratio function is adopted to speed up the MS_CMAC training. Several numerical problems are considered to test the improved MS_CMAC. The computed results indicate that a simplified UFN model can produce good initial values of the virtual grid-distributed data points to aggrandize MS_CMAC training. The MS_CMAC prediction is also improved by using the initialized virtual grid-distributed data points.

A macro structure cerebellar model articulation controller (CMAC) or MS_CMAC was developed by connecting several one-dimensional (1-D) CMACs as a tree structure, which decomposes a multidimensional problem into a set of 1-D subproblems, to reduce the computational complexity in multidimensional CMAC. Additionally, a trapezium scheme is proposed to assist MS_CMAC to model nonlinear systems. However, this trapezium scheme cannot perform a real smooth interpolation, and its working parameters are obtained through cross-validation. A quadratic splines scheme is developed herein to replace the trapezium scheme in MS_CMAC, named high-order MS_CMAC (HMS_CMAC). The quadratic splines scheme systematically transforms the stepwise weight contents of CMACs in MS_CMAC into smooth weight contents to perform the smooth outputs. Test results affirm that the HMS_CMAC has acceptable generalization in continuous function-mapping problems for nonoverlapping association in training instances. Nonoverlapping association in training instances not only significantly reduces the number of training instances needed, but also requires only one learning cycle in the learning stage.