Operational matrix based set-membership method for fractional order systems parameter identification

Abstract In this paper, a new method is proposed to identify the coefficients and differentiation orders of fractional order systems with measurement noise. The proposed method combines the operational matrix method and the set-membership method. First, the block pulse function operational matrix of the fractional differentiation is used to convert the fractional order system to an algebraic system. Then, the coefficients and differentiation orders are simultaneously estimated through a nest loop optimization process, where the optimal bounding ellipsoid set-membership algorithm is utilized to estimate the system’s coefficients and the orders are estimated with the interior-point method. The proposed method can accurately estimate the coefficients and differentiation orders of fractional order systems under any bounded measurement noise with less computational effort. Experimental results demonstrate the effectiveness of the proposed method.