Ensemble Optimal Control of Control-Affine Systems with Uncertain Initial Conditions
DOI:
https://doi.org/10.5540/03.2026.012.01.0280Keywords:
Optimal Control, Uncertain Systems, Riemann-Stieltjes Problem, Pontryagin Maximum Principle, Ensemble ControlAbstract
We explore optimal control problems in systems with uncertain parameters that follow a probability distribution, aiming to optimize average performance. Known as Riemann-Stieltjes, average, or ensemble optimal control, these problems are essential when parameter uncertainty plays a significant role. We establish necessary conditions and analyze feedback control structures for control-affine systems. By extending the Pontryagin Maximum Principle through a Hilbert space approach, we characterize singular arcs, and numerical examples demonstrate the practical applicability of our findings.
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References
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