磁悬浮列车随机非线性最优控制研究

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关键词：磁悬浮列车；控制策略；随机激励；非线性随机动力学

中图分类号：U260

DOI：10.3969/j.issn.1004-132X.2025.11.013 开放科学（资源服务）标识码（OSID）：

Abstract：To improve the stability of the maglev systems，the stochastic differential equations for the controlled maglev systems were established based on Hamilton's theory，where the nonlinear characteristics of the aerodynamic lift and levitation forces were taken into account.The dynamic planning equations for an optimal control strategy were developed with the objectives of maximizing the reliability，extending the longest average first-passage time，and minimizing the maximum Lyapunov exponent. The results show that the conditional reliability of the maglev systems may be improved and the average first-passage time prolonged by considering the joint action of PD control and optimal control. Moreover，the maximum Lyapunov exponent is always negative，satisfying the conditions for the trivial solution of the maglev systems to be asymptotically stable with a probability of1. After optimal control，the joint probability density of the systems undergoes a change in behavior，which improves the system's stability. When the intensity of Gaussian white noise is low，the optimal control strategy for maximum reliability has better performance indicators. However，the strategy for minimum the maximum Lyapunov exponent only exhibits good performance within a certain range.The study of the optimal control problem of the maglev trains provides a theoretical basis forimprovingthe train's stability and prolonging the timeuntil the first-passage failure occurs.

Key words：maglev train; control strategy;random excitation； nonlinear stochastic dynamics

0 引言

磁悬浮列车是一种新型的交通运输方式[]。（剩余14844字）