Optimal Input Design for Fractional-Order System Identification Using an LMI-Based Frequency Error Criterion

This paper presents a novel approach to optimal input signal design for open-loop fractional-order system identification, using an integer-order approximation of the fractional operators to minimize the average input power. This is obtained by formulating the problem as an LMI (Linear Matrix Inequality) optimization problem with the limitation of achieving at least a specified model accuracy. The ORA (Oustaloup Recursive Approximation) method has been employed to model the fractional-order differentiation operator in discrete integer-order Output Error model form. The optimal input design is executed using finite-dimensional FIR (Finite Impulse Response) filter spectrum parameterization, where the decision variables are calculated through convex optimization. The A-optimality criterion has been used to examine the relationship between the input signal spectrum power and the accuracy of estimated models. Finally, numerical examples illustrate the proposed approach, confirming the method’s suitability for fractional-order system identification.