ADAPTIVE MITTAG-LEFFLER STABILIZATION OF A CLASS OF FRACTIONAL ORDER UNCERTAIN NONLINEAR SYSTEMS

作者：Wang, Qiao^*; Zhang, Jianliang; Ding, Dongsheng; Qi, Donglian

来源：Asian Journal of Control, 2016, 18(6): 2343-2351.

DOI：10.1002/asjc.1296

• Fractional order systems
• uncertainty
• Lyapunov function
• Mittag-Leffler stability
• adaptive control
• nonlinearity

This paper deals with the stabilization of a class of commensurate fractional order uncertain nonlinear systems. The fractional order system concerned is of the strict-feedback form with uncertain nonlinearity. An adaptive control scheme combined with fractional order update laws is proposed by extending classical backstepping control to fractional order backstepping scheme. The asymptotic stability of the closed-loop system is guaranteed under the construction of fractional Lyapunov functions in the sense of generalized Mittag-Leffler stability. The fractional order nonlinear system investigated can be stabilized asymptotically globally in presence of arbitrary uncertainty. Finally illustrative examples and numerical simulations are performed to verify the effectiveness of the proposed control scheme.

• 出版日期2016-11
• 单位浙江大学