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arXiv · 2505.06204

Average Optimal Control of Uncertain Control-Affine Systems

M. Soledad Aronna·Gabriel de Lima Monteiro·Oscar Sierra Fonseca
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Abstract

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.

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M. Soledad Aronna, Gabriel de Lima Monteiro, Oscar Sierra Fonseca. 2025-05-09. Average Optimal Control of Uncertain Control-Affine Systems. https://doi.org/10.1007/s11228-025-00784-0

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