Identification of nonlinear discrete-time systems using raised-cosine radial basis function networks

Abstract

An effective technique for identifying nonlinear discrete-time systems using raised-cosine radial basis function (RBF) networks is presented. Raised-cosine RBF networks are bounded-input bounded-output stable systems, and the network output is a continuously differentiable function of the past input and the past output. The evaluation speed of an n-dimensional raised-cosine RBF network is high because, at each discrete time, at most 2n RBF terms are nonzero and contribute to the output. As a consequence, raised-cosine RBF networks can be used to identify relatively high-order nonlinear discrete-time systems. Unlike the most commonly used RBFs, the raised-cosine RBF satisfies a constant interpolation property. This makes raised-cosine RBF highly suitable for identifying nonlinear systems that undergo saturation effects. In addition, for the important special case of a linear discrete-time system, a first-order raised-cosine RBF network is exact on the domain over which it is defined, and it is minimal in terms of the number of distinct parameters that must be stored. Several examples, including both physical systems and benchmark systems, are used to illustrate that raised-cosine RBF networks are highly effective in identifying nonlinear discrete-time systems.