Adaptive sliding mode output tracking control based-FODOB for a class of uncertain fractional-order nonlinear time-delayed systems

• Published in: Science China. Technological sciences Vol. 63; no. 9; pp. 1854 - 1862
• Main Authors: Wang, Zhen, Wang, XinHe, Xia, JianWei, Shen, Hao, Meng, Bo
• Format: Journal Article
• Language: English
• Published: Beijing Science China Press 01.09.2020; Springer Nature B.V
• Subjects: Adaptive control; Engineering; Nonlinear systems; Sliding mode control; Time delay systems; Tracking control; Tracking errors; Tracking problem; adaptive sliding mode control; time-delay; disturbance-observer; uncertainty; fractional-order
• ISSN: 1674-7321; 1869-1900
• DOI: 10.1007/s11431-019-1476-4

An adaptive sliding mode control (ASMC) method, based on fractional-order disturbance-observer (FODOB), is presented for a class of fractional-order nonlinear time-delay systems (FONTDS) with uncertainties to solve the target output tracking problem. The external disturbances are estimated by FODOB, and the unknown internal perturbations of the system are adaptively estimated by sliding mode control (SMC). Furthermore, Gronwall’s inequality approach is used to ensure that the output tracking error is uniformly bounded for FONTDS. Firstly, a fractional-order sliding mode control (FOSMC) based FODOB is proposed for a fractional-order linear time-delay system (FOLTDS). Secondly, combined with adaptive estimation, the ASMC of FONTDS is studied. Finally, a numerical example of FONTDS is used to verify the effectiveness of the proposed methods.