Consider the problem of identifying the nonlinear discrete-time system in (9.9.4) using a raised-cosine RBF network. Let the number of past inputs be m = 1 and the number of past outputs be n = 1. Suppose the range of values for the inputs is a = [-2, 2], and the range of values for the outputs is b = [-3, 3]. Let the number of grid points per dimension be d = 4.
(a) Find the domain U of the function f.
(b) What is the total number of grid points?
(c) What is the grid point spacing in the x direction and in the y direction?
(d) For each u, what is the maximum number of nonzero terms in the RBF network output?
(e) Consider the following state vector. Find the vector subscripts of the vertices of the grid element containing u.