Estimation Methods for Fractional-Order Systems

This chapter deals with the design of estimation algorithms for fractional-order systems (FOSs). In particular, asymptotic and nonasymptotic methods, namely observer-based method and the modulating functions-based method, are presented, respectively. The first approach proposes an adaptive observer to estimate jointly the pseudostate and the parameters of nonlinear commensurate FOSs represented by a pseudostate representation. However, the second approach is concerned with linear noncommensurate FOSs represented by an input-output mapping and for which a modulating functions-based method is introduced to estimate the parameters and fractional differentiation orders. The analytical derivations for both techniques are provided. Moreover, their performance is illustrated through some numerical simulations.