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Prescribed-Time Control of Stochastic Nonlinear Systems with Reduced Control Effort

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Abstract

A new prescribed-time state-feedback design is presented for stochastic nonlinear strict-feedback systems. Different from the existing stochastic prescribed-time design where scaling-free quartic Lyapunov functions or scaled quadratic Lyapunov functions are used, the design is based on new scaled quartic Lyapunov functions. The designed controller can ensure that the plant has an almost surely unique strong solution and the equilibrium at the origin of the plant is prescribed-time mean-square stable. After that, the authors redesign the controller to solve the prescribed-time inverse optimal mean-square stabilization problem. The merit of the design is that the order of the scaling function in the controller is reduced dramatically, which effectively reduces the control effort. Two simulation examples are given to illustrate the designs.

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Author information

Authors and Affiliations

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

    Wuquan Li

  2. Department of Mechanical and Aerospace Engineering, University of California, San Diego, La Jolla, CA, 92093, USA

    Miroslav Krstic

Authors
  1. Wuquan Li
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  2. Miroslav Krstic
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Corresponding authors

Correspondence to Wuquan Li or Miroslav Krstic.

Additional information

This research is supported by the National Natural Science Foundation of China under Grant No. 61973150, the Young Taishan Scholars Program of Shandong Province of China under Grant No. tsqn20161043, Shandong Provincial Natural Science Foundation for Distinguished Young Scholars under Grant No. ZR2019JQ22, and Shandong Province Higher Educational Excellent Youth Innovation team under Grant No. 2019KJN017.

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Li, W., Krstic, M. Prescribed-Time Control of Stochastic Nonlinear Systems with Reduced Control Effort. J Syst Sci Complex 34, 1782–1800 (2021). https://doi.org/10.1007/s11424-021-1217-7

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  • DOI: https://doi.org/10.1007/s11424-021-1217-7

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