High-order MS CMAC neural network

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.