An identification method of nonlinear systems by volterra series

Abstract

AbstractNumerical models whose input‐output relations are expressed by Volterra series, are used to identify nonlinear systems from observed set of inputs and outputs according to given evaluation criterion. Parameters of systems to be identified are Volterra kernels of various orders. Since these kernels are multivariable functions, considerable calculation and memory capacities are required for identification. This paper presents a method without Volterra series which are multivariable functions for identification and output estimation. Our identification method follows the report by Hsieh; the evaluation function is expressed using inner products in Hilbert space, employing operators from fixed input and the Hilbert space to which outputs belong. Next, the Volterra kernel of each order is regarded as a mapping from adjoint space, and the optimization is done for one variable function in adjoint space. The computing method is as follows: the problem in Hilbert space is replaced by a problem in a finite‐dimensional vector space by discretizing the time axis, the orthogonal vector system is obtained, and the optimization by one‐dimensional time sequence is done. Afterward, it is shown that the output estimation can be done for other inputs without obtaining Volterra kernels which are multivariable functions, by using the adjoint solution obtained as described in the foregoing, and constructing its computer algorithm.