Continuous Time System Identification Using Shifted Chebyshev Polynomials

A new instrumental variables based identification procedure is introduced to estimate linear and nonlinear continuous time models using a shifted Chebyshev basis in the presence of noise. Orthogonal polynomials have been used by many authors in continuous time system analysis, identification and control. By introducing an operational matrix continuous time differential equations can be transferred to algebraic forms, from which the parameters can be estimated using least squares. In the system identification problem, however, the application of most of these approaches in the literature have ignored noise or assumed that the noise level is unrealistically low. In this letter shifted Chebyshev polynomials will be applied to the identification of continuous time linear and nonlinear systems. If the noise contained in the measured output were ignored the estimates would be biased. An Instrumental Variable method is introduced to overcome the bias problem.