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Prescribed-time stabilization and inverse optimal control of stochastic high-order nonlinear systems

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Abstract

This paper investigates the prescribed-time state-feedback stabilization and prescribed-time inverse optimality problems for stochastic high-order nonlinear systems. First, a time-varying controller is designed by developing scaled quartic Lyapunov functions, which can guarantee that the system has a unique strong solution almost surely on the prescribed interval for any system initial conditions and that the states and the control converge to the origin in a mean-square form within the prescribed time. Then, the controller is redesigned to address the problem of prescribed-time inverse optimal mean-square stabilization. Finally, a concrete example is provided to confirm the efficiency of the proposed design schemes.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant No. 62373179), Taishan Scholars Program of Shandong Province of China (Grant No. tstp20221133), Fundamental Research Projects of Science & Technology Innovation and Development Plan in Yantai City (Grant No. 2023JCYJ051), and Special Supporting Funding for Leading Talents Above Provincial Level in Yantai City.

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Authors and Affiliations

  1. School of Mathematics and Statistics Science, Ludong University, Yantai, 264025, China

    Ran Liu, Hui Wang & Wuquan Li

Authors
  1. Ran Liu
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  2. Hui Wang
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  3. Wuquan Li
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Corresponding authors

Correspondence to Hui Wang or Wuquan Li.

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Liu, R., Wang, H. & Li, W. Prescribed-time stabilization and inverse optimal control of stochastic high-order nonlinear systems. Sci. China Inf. Sci. 67, 122202 (2024). https://doi.org/10.1007/s11432-022-3842-2

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  • DOI: https://doi.org/10.1007/s11432-022-3842-2

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