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<p>This paper investigates the adaptive fixed-time stabilization problem for a class of strict-feedback stochastic nonlinear systems with unknown parameter vectors and unbounded but estimable nonlinear boundary functions. By employing distributed Lyapunov functions for state-space partitioning and distinct error transformations, this paper ensures system states converge to zero in a fixed-time regardless of initial conditions and stochastic disturbances. This paper introduces a distributed controller design that uniquely combines adaptive backstepping with the adding one power integrator method, restricting tracking errors to a positive invariant set to avoid the inherent singularity risks in traditional backstepping-based stochastic control. Unlike existing fixed-time control approaches for stochastic systems, which are typically limited to bounded uncertainties or rely on fuzzy logic with high computational overhead, this paper promotes a method handles fully unknown and unbounded nonlinear boundaries by means of adaptive estimation, thereby completely eliminating the redundant terms inherent in fuzzy approximations and enhancing 30–40% computing efficiency. Two simulations evaluate the robustness and efficacy of the proposed method under diverse initial conditions and stochastic disturbances, using settling time within the theoretically derived fixed convergence time to validate its practical applicability.</p>

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Distributed adaptive stabilization for stochastic nonlinear systems with unknown boundaries: a novel fixed-time stability in probability

  • 期刊论文

  • 发表日期：

    2025年6月17日

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  • Jiahui Zhu,
  • Liping Xie,
  • Kanjian Zhang

摘要

This paper investigates the adaptive fixed-time stabilization problem for a class of strict-feedback stochastic nonlinear systems with unknown parameter vectors and unbounded but estimable nonlinear boundary functions. By employing distributed Lyapunov functions for state-space partitioning and distinct error transformations, this paper ensures system states converge to zero in a fixed-time regardless of initial conditions and stochastic disturbances. This paper introduces a distributed controller design that uniquely combines adaptive backstepping with the adding one power integrator method, restricting tracking errors to a positive invariant set to avoid the inherent singularity risks in traditional backstepping-based stochastic control. Unlike existing fixed-time control approaches for stochastic systems, which are typically limited to bounded uncertainties or rely on fuzzy logic with high computational overhead, this paper promotes a method handles fully unknown and unbounded nonlinear boundaries by means of adaptive estimation, thereby completely eliminating the redundant terms inherent in fuzzy approximations and enhancing 30–40% computing efficiency. Two simulations evaluate the robustness and efficacy of the proposed method under diverse initial conditions and stochastic disturbances, using settling time within the theoretically derived fixed convergence time to validate its practical applicability.