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<p>This work studies optimal control problems of systems with uncertain, probabilistically distributed parameters to optimize average performance. Known as <i>Riemann-Stieltjes, average,</i> or <i>ensemble optimal control,</i> this kind of problem is crucial when parameter uncertainty matters. We derive necessary optimality conditions and characterize feedback controls for control-affine systems. Two scenarios are examined: known initial conditions (finite-dimensional case) and uncertain initial conditions (infinite-dimensional framework). The Pontryagin Maximum Principle is extended using a Hilbert space formulation.</p>

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Average Optimal Control of Uncertain Control-Affine Systems

  • 期刊论文

  • 发表日期：

    2025年12月11日

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  • M. Soledad Aronna,
  • Gabriel de Lima Monteiro,
  • Oscar Sierra Fonseca

摘要

This work studies optimal control problems of systems with uncertain, probabilistically distributed parameters to optimize average performance. Known as Riemann-Stieltjes, average, or ensemble optimal control, this kind of problem is crucial when parameter uncertainty matters. We derive necessary optimality conditions and characterize feedback controls for control-affine systems. Two scenarios are examined: known initial conditions (finite-dimensional case) and uncertain initial conditions (infinite-dimensional framework). The Pontryagin Maximum Principle is extended using a Hilbert space formulation.