Aiming at predefined-time synchronization for chaotic systems, a new predefined-time sliding mode control method is proposed. First, based on the definition of predefined-time stability, a novel predefined-time inequality is proposed, along with a detailed mathematical proof. This inequality differs from existing Lyapunov inequalities and offers greater flexibility. Second, a new sliding mode surface and sliding mode controller are proposed based on this inequality. Since the sliding mode controller introduced in this paper is tunable, the actual convergence time can be adjusted freely within the predefined time. Finally, two sets of numerical simulations demonstrate that the proposed method offers advantages in terms of short synchronization time and high regulatory performance compared to traditional predefined-time sliding mode control, finite-time sliding mode control, and fixed-time sliding mode control.
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December 2024
Research Article|
December 03 2024
Novel predefined-time stability theory and its application in sliding mode control of synchronizing chaotic systems
Jingang Liu
;
Jingang Liu
(Funding acquisition, Project administration, Writing – review & editing)
School of Mathematics and Computational Science, Xiangtan University
, Xiangtan 411105, China
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Ruiqi Li
Ruiqi Li
a)
(Conceptualization, Data curation, Methodology, Writing – original draft)
School of Mathematics and Computational Science, Xiangtan University
, Xiangtan 411105, China
a)Author to whom correspondence should be addressed: [email protected]
Search for other works by this author on:
a)Author to whom correspondence should be addressed: [email protected]
Rev. Sci. Instrum. 95, 124702 (2024)
Article history
Received:
September 29 2024
Accepted:
November 11 2024
Citation
Jingang Liu, Ruiqi Li; Novel predefined-time stability theory and its application in sliding mode control of synchronizing chaotic systems. Rev. Sci. Instrum. 1 December 2024; 95 (12): 124702. https://doi.org/10.1063/5.0241261
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