<p>The practical systems in engineering always have complicated structures and constantly suffer from uncertainty and multiple time delays, which bring many challenges to system control. Considering this issue, this article discusses the adaptive control issue of stochastic nonlinear system (SNS) with multiple time delays, unknown parameters, and complicated structure. By introducing a dynamic-gain-based transformation, a new dynamic system is obtained first. Then, the nominal system is considered and a stabilization control design method is developed. By exploring the homogeneous domination method and Lyapunov-Krasovskii (L-K) theory, a dynamic adaptive controller is designed to guarantee that the system has a unique solution and the system is globally stable in probability. Finally, the effectiveness of the presented control strategy is demonstrated with two examples.</p>

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A dynamic-gain-based adaptive homogeneous control approach of high-order stochastic nonlinear system with time-varying delays

  • Zhen-Guo Liu,
  • Ziwen Jiang,
  • Lingrong Xue,
  • Weihai Zhang

摘要

The practical systems in engineering always have complicated structures and constantly suffer from uncertainty and multiple time delays, which bring many challenges to system control. Considering this issue, this article discusses the adaptive control issue of stochastic nonlinear system (SNS) with multiple time delays, unknown parameters, and complicated structure. By introducing a dynamic-gain-based transformation, a new dynamic system is obtained first. Then, the nominal system is considered and a stabilization control design method is developed. By exploring the homogeneous domination method and Lyapunov-Krasovskii (L-K) theory, a dynamic adaptive controller is designed to guarantee that the system has a unique solution and the system is globally stable in probability. Finally, the effectiveness of the presented control strategy is demonstrated with two examples.