Adaptive order and parameter estimation in fractional linear systems by approximate gradient and least squares methods*

Adaptive parameter estimation schemes for linear fractional-order processes of commensurate type are illustrated in the present paper. A key feature of the proposed schemes is the utilization of appropriate variable-order fractional filters. A combined gradient/least-squares scheme for simultaneously estimating the commensurate order and the remaining process parameters is considered. Certain approximations are introduced in order to reduce the computational burden of the estimator. Theoretical results are validated by means of thoroughly discussed simulation examples.