Adaptive identification of the commensurate order in fractional processes by means of variable-order operators

A gradient-based algorithm for the on-line continuous estimation of the commensurate order in linear fractional order processes is presented. A key aspect of the proposed methodology is the use of appropriate variable-order fractional filters, and linear Laplace operators of logarithmic type, within the estimation mechanism. A Lyapunov based analysis will be provided for deriving appropriate sufficient conditions guaranteeing the parameter convergence property. Realization issues associated to the involved variable order operators are discussed, and a fully developed analysis and design example, accompanied by relevant simulation results, is provided to support the presented theory.