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Adaptive prescribed performance control for state constrained stochastic nonlinear systems with unknown control direction: a novel network-based approach

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Abstract

In this paper, the tracking control problem of the state constrained stochastic nonlinear systems with unknown control direction is studied, and a novel adaptive prescribed performance control (PPC) approach is developed with the help of the multi-dimensional Taylor network (MTN). Firstly, a performance function is introduced into the first step of backstepping to ensure transient performance under state constraints. Secondly, the tangent time-varying barrier Lyapunov functions (tan-TVBLFs) are constructed to prevent all states from violating the given time-varying boundary. Thirdly, the MTNs are employed to estimate the unknown nonlinearity in the process of controller design, and a new adaptive PPC strategy is designed. Then, the Lyapunov stability theorem is used to prove that the closed-loop system is semi-global uniformly ultimately bounded (SGUUB) in probability, and the tracking error can be kept in an adjustable small neighborhood of the origin. Finally, the effectiveness of the proposed scheme is verified by the simulation of a numerical example and an actual control system.

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Funding

This work was supported by the Shandong Provincial Natural Science Foundation, China (No. ZR2020QF055).

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Author notes

  1. Yu-Qun Han and Na Li have contributed equally to this work.

Authors and Affiliations

  1. School of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao, 266061, China

    Yu-Qun Han, Na Li, Dong-Mei Wang, Ya-Feng Zhou & Shan-Liang Zhu

  2. Research Institute for Mathematics and Interdisciplinary Sciences, Qingdao University of Science and Technology, Qingdao, 266061, China

    Yu-Qun Han & Shan-Liang Zhu

Authors
  1. Yu-Qun Han
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  2. Na Li
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  3. Dong-Mei Wang
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  4. Ya-Feng Zhou
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Correspondence to Shan-Liang Zhu.

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Han, YQ., Li, N., Wang, DM. et al. Adaptive prescribed performance control for state constrained stochastic nonlinear systems with unknown control direction: a novel network-based approach. Neural Comput & Applic 36, 2737–2748 (2024). https://doi.org/10.1007/s00521-023-09125-4

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