PARAMETER-IDENTIFICATION OF TIME-VARYING SYSTEM VIA GENERALIZED ORTHOGONAL POLYNOMIALS

An effective method is presented of using generalized orthogonal polynomials (GOPs) for identifying the parameters of a process whose behaviour can be modelled by a linear differential equation with time-varying coefficients in the form of finite-order polynomials. It is based on the repeated integration of a differential equation and the integration operational matrix of the GOP which can represent all kinds of individual orthogonal polynomials. By expanding the state function and control function into a series of GOPs, the differential input-output equation is converted into a set of overdetermined linear algebraic equations. The unknown parameters are evaluated by using the least-squares method in conjunction with an orthogonal polynomial expansion. An example is given to illustrate the usefulness of the method and very satisfactory results are obtained.