A novel algorithm on adaptive backstepping control for a class of uncertain fractional-order systems: an ADRC approach

This article aims at presenting a novel algorithm on adaptive control for commensurate fractional-order systems(FOSs) by employing active disturbance rejection control(ADRC)approach. Using adaptive controller and ADRC together makes the proposed controller available to handle both parametric and nonlinear uncertainties that are usually occur in wide class of systems. In order to estimate matched and mismatched nonlinear uncertainties, fractional-order extended state observer(FO-ESO) is employed in each channel, then, parametric uncertainties are estimated by adaptive backstepping method that provides a control law to track the desired signal. Mittag-Leffler stability of control system is verified in control design procedure and finally, the advantages of the proposed controller are demonstrated by numerical example.