Adaptive Mittag-Leffler stabilization of commensurate fractional-order nonlinear systems

In this paper, a new adaptive control technique called adaptive fractional-order backstepping is proposed, for a class of commensurate fractional-order nonlinear systems with uncertain constant parameters. Using the adaptive fractional-order backstepping as a basic design tool, we show how to explicitly construct an adaptive feedback control laws that solve the Mittag-Leffler stabilization problem of uncertain commensurate fractional-order nonlinear systems. The global convergence of the closed-loop systems is guaranteed in the sense of Mittag-Leffler stability. The efficiency of the proposed technique is demonstrated in simulation finally.