A learning technique for Volterra series representation

Abstract

This paper presents a method of system identification based upon the techniques of pattern recognition. The method developed is an on-line error-correcting procedure which provides the coefficients of the Volterra series representation of the system. The systems considered are those with finite settling time and piecewise constant inputs. The method is extremely general, identifying both linear and nonlinear systems in the presence of noise, without the requirement of special test signals. The theoretical basis for this method lies in the observation that system identification is a special case of the general theory of pattern recognition. A system is treated as a transformation from the set of past inputs to the real line, the system output. The Volterra expansion treats this transformation as a hypersurface, the shape of which is determined by the Volterra kernels. However, the techniques of pattern recognition produce this type of surface as the discriminant function between pattern classes. Furthermore, these surfaces are iteratively obtained as more data are available. Consequently, the computational difficulties, which are encountered in obtaining the Volterra kernels, are circumvented by this iterative learning procedure.