Variable-Order Fractional Operators for Adaptive Order and Parameter Estimation

Adaptive parameter estimation schemes for linear fractional-order processes of commensurate type are illustrated in the present note. A gradient-based scheme for commensurate order estimation is outlined first, and a combined gradient/least-squares scheme for simultaneously estimating the commensurate order and the remaining process parameters is finally considered. A key feature of the proposed schemes is the utilization of appropriate variable-order fractional filters. Theoretical results are validated by means of thoroughly discussed simulation examples.