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Variable speed exponential control of a class of chaotic systems with external disturbances via sliding mode method

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Abstract

The problem of exponential control of a class of chaotic systems having external disturbances is addressed in this paper. By using a series of state variable transformations, the complicated n-order system is converted to a two-order system. With the second-order system obtained, a new non-singular fast sliding mode surface which makes the trajectories finite-timely converge to the origin is proposed. For realising the exponential control, a novel controller is presented to drive the states of the controlled system to the sliding surface. Unlike the previous literature, the convergence rate of the system can be adjusted by a specified parameter \(\lambda \) in the controller. Besides, a new slide mode manifold which has no signal functions is designed, and both chatter phenomenon and singular problems occurring in the controller can be alleviated well. A chaotic system is applied to simulations to testify the validity of the presented approach.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 11761050).

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Authors and Affiliations

  1. Department of Mathematics, Nanchang University, Nanchang,  330031, People’s Republic of China

    Haipeng Su, Runzi Luo, Jiaojiao Fu & Meichun Huang

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  1. Haipeng Su
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  2. Runzi Luo
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  3. Jiaojiao Fu
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  4. Meichun Huang
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Correspondence to Runzi Luo.

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Su, H., Luo, R., Fu, J. et al. Variable speed exponential control of a class of chaotic systems with external disturbances via sliding mode method. Pramana - J Phys 96, 161 (2022). https://doi.org/10.1007/s12043-022-02409-9

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  • DOI: https://doi.org/10.1007/s12043-022-02409-9

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