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Robust Fixed Time Control of a Class of Chaotic Systems with Bounded Uncertainties and Disturbances

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Abstract

This paper investigates the fixed time control of a class of chaotic systems with uncertainties and disturbances via a novel fixed time theorem. By using variable substitution to calculate definite integral, a sufficient condition for fixed-time stability is firstly derived. Then, based on the given fixed time stable theory, a new nonlinear slide mode surface is proposed. By using a novel robust controller, the system’s state trajectories are driven to its origin in a fixed time which is independent on the initial value. The control strategy is applied to the permanent magnet synchronous motor (PMSM) chaotic system, and the results of numerical simulation demonstrate the effectiveness of the proposed schemes.

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Funding

This work was jointly supported by the National Natural Science Foundation of China under Grant Nos. 11761050 and 11361043, the Natural Science Foundation of Jiangxi Province under Grant No. 20161BAB201008 and the Graduate Innovative Foundation of Jiangxi Province under Grant No. YC2020-B007.

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Authors and Affiliations

  1. Department of Mathematics, the School of Sciences, Nanchang University, Nanchang, 330031, China

    Haipeng Su, Runzi Luo, Meichun Huang & Jiaojiao Fu

Authors
  1. Haipeng Su
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  2. Runzi Luo
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  3. Meichun Huang
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  4. Jiaojiao Fu
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Corresponding author

Correspondence to Runzi Luo.

Additional information

Haipeng Su received his B.S. degree in operational research and cybernetics from Nanchang University, Nanchang, China, in 2019. He is currently pursuing a Ph.D. degree from Nanchang University, Nanchang, China. His current research interests include nonlinear dynamics, complex network, chaotic control and synchronization.

Runzi Luo received his Ph.D. degree in operational research and cybernetics from Shanghai University, Shanghai, China, in 2005. He is currently a Professor with the Department of Mathematics, Nanchang University, Nanchang, China. His research interests include nonlinear systems, complex networks, stability theory and applied mathematics, chaos synchronization and secure communication.

Meichun Huang is currently a master’s degree student of Applied mathematics in Nanchang University, Nanchang, China. Her research interests include nonlinear control, chaos control and synchronization.

Jiaojiao Fu is currently a master’s degree student of Applied mathematics in Nanchang University, Nanchang, China. Her research interests include memristive neural networks, chaos control and synchronization.

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Su, H., Luo, R., Huang, M. et al. Robust Fixed Time Control of a Class of Chaotic Systems with Bounded Uncertainties and Disturbances. Int. J. Control Autom. Syst. 20, 813–822 (2022). https://doi.org/10.1007/s12555-020-0782-1

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  • DOI: https://doi.org/10.1007/s12555-020-0782-1

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