Analysis and parameter estimation of bilinear systems via generalized orthogonal polynomials

Abstract

Abstract An effective method of using generalized orthogonal polynomials (GOP) for analysing and identifying the parameters of a process whose behaviour can be modelled by a bilinear equation is presented. The integration operational matrix and the operational matrix for the product of ti with the GOP vector are derived. These two kinds of operational matrices of the GOP are related to any type of individual orthogonal polynomial. By expanding the state and control functions into a series of GOP, the bilinear equation can be converted into a set of linear algebraic equations. The expansion coefficients of state variables are solved from these linear algebraic equations. The unknown parameters are evaluated by using the least squares method in conjunction with the individual orthogonal polynomial expansion. Two examples are given to illustrate the validity of the method. Very satisfactory results are obtained.