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<p>This article presents the classical optimal control methods for the numerical solutions of optimal control problems with interval formulations. Two computational methods are developed by extending the Hamilton–Jacobi–Bellman equation and the Pontryagin’s principle for the interval optimal control problems, and that appropriate controller has been derived through both techniques discussed. Our approach leverages single-level constrained interval arithmetic to effectively mitigate the dependency issue, ensuring tighter and more reliable interval solutions. In addition, the numerical examples focus exclusively on linear-quadratic models, one in a single dimension and the other in two dimensions, that demonstrate the superior performance and accuracy of the proposed methods against conventional approaches.</p>

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Optimality conditions and numerical methods for optimal control problems with interval uncertainty

  • 期刊论文

  • 发表日期：

    2026年4月21日

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  • Samaneh Soradi-Zeid,
  • Mehdi Allahdadi,
  • Tahereh Shokouhi

摘要

This article presents the classical optimal control methods for the numerical solutions of optimal control problems with interval formulations. Two computational methods are developed by extending the Hamilton–Jacobi–Bellman equation and the Pontryagin’s principle for the interval optimal control problems, and that appropriate controller has been derived through both techniques discussed. Our approach leverages single-level constrained interval arithmetic to effectively mitigate the dependency issue, ensuring tighter and more reliable interval solutions. In addition, the numerical examples focus exclusively on linear-quadratic models, one in a single dimension and the other in two dimensions, that demonstrate the superior performance and accuracy of the proposed methods against conventional approaches.