Distributed parameter system identification via Walsh functions

Abstract

A method is presented for estimating the parameters, and the initial and boundary conditions of a linear time-invariant distributed-parameter system. The approach followed begins by converting the assumed partial differential equation model into an integral equation. Subsequently, the input and output signals as well as the unknown initial and boundary conditions are expanded in Walsh series and are introduced into the integral equation, whereupon equating coefficients of like Walsh functions, a linear system of algebraic equations is derived. This system is then solved to yield an estimate of the distributed parameter model.