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<p>To synchronize the output of the van der Pol generator with a specified periodic signal, this research suggests a min-max robust control design strategy based on the neural dynamic programming approach that makes use of continuous differential neural networks (DNNs). The synchronization process is considered when modeling uncertainties and external disturbances exist in the sensing devices. Robust control may be achieved by using the min-max formulation of the dynamic programming approach. The maximization procedure, which leads to the worst-case scenario, is considered with respect to the uncertainties supplied. In contrast, the minimization procedure, or optimization, is carried out by adjusting the generator-controlled parameters. The DNN approximation of a viscosity solution for the min-max version of the Hamilton–Jacobi–Bellman (HJB) equation characterizes the corresponding robust controller, a strategy that simplifies the calculus of the differentiable value function based on the HJB equation. The proposed learning law determines how the DNN’s weights change over time. The weight dynamics terminal requirements are satisfied using a modified Kiefer–Wolfowitz recurrent method. A numerical example simulation of the van der Pol generator demonstrates the application of the proposed controller, highlighting the combination of the Min and Max operations to resolve the robust optimal control of such a class of electrical circuits.</p>

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Robust synchronization of van der Pol voltage generator using neural approximation of dynamic programming min-max viscosity solution with state and control constraints

  • 期刊论文

  • 发表日期：

    2026年7月22日

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  • Sebastian Noriega-Marquez,
  • Alejandra Hernandez-Sanchez,
  • Alexander Poznyak,
  • Isaac Chairez

摘要

To synchronize the output of the van der Pol generator with a specified periodic signal, this research suggests a min-max robust control design strategy based on the neural dynamic programming approach that makes use of continuous differential neural networks (DNNs). The synchronization process is considered when modeling uncertainties and external disturbances exist in the sensing devices. Robust control may be achieved by using the min-max formulation of the dynamic programming approach. The maximization procedure, which leads to the worst-case scenario, is considered with respect to the uncertainties supplied. In contrast, the minimization procedure, or optimization, is carried out by adjusting the generator-controlled parameters. The DNN approximation of a viscosity solution for the min-max version of the Hamilton–Jacobi–Bellman (HJB) equation characterizes the corresponding robust controller, a strategy that simplifies the calculus of the differentiable value function based on the HJB equation. The proposed learning law determines how the DNN’s weights change over time. The weight dynamics terminal requirements are satisfied using a modified Kiefer–Wolfowitz recurrent method. A numerical example simulation of the van der Pol generator demonstrates the application of the proposed controller, highlighting the combination of the Min and Max operations to resolve the robust optimal control of such a class of electrical circuits.