Adaptive Sliding Mode Control for Uncertain General Fractional Chaotic Systems

Yonggui Kao, Changhong Wang, Hongwei Xia and Yue Cao
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Yonggui Kao: Harbin Institute of Technology (Weihai), Department of Mathematics
Changhong Wang: Harbin Institute of Technology, School of Astronautics
Hongwei Xia: Harbin Institute of Technology, School of Astronautics
Yue Cao: Harbin Institute of Technology (Weihai), Department of Mathematics

Chapter Chapter 2 in Analysis and Control for Fractional-order Systems, 2024, pp 13-30 from Springer

Abstract: Abstract This chapter focuses on the Lyapunov stability analysis of general fractional differential systems (GFDSs), as well as adaptive sliding mode control (ASMC) of uncertain general fractional chaotic systems (UGFCSs) with uncertainty and external disturbances. Initially, the existence and uniqueness of solutions and the Lyapunov stability criterion for GFDSs are presented and verified. Furthermore, general fractional integral type sliding surfaces and reaching law are established. Based on the proposed stability criterion, it is shown that the states of UGFCSs can reach the sliding surface and asymptotically converge to zero along the sliding surface. Lastly, the efficacy and efficiency of the proposed fractional controllers are demonstrated by numerical simulations.

Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-99-6054-5_2

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DOI: 10.1007/978-981-99-6054-5_2

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