Convergence Rates for Ensemble-Based Solutions to Optimal Control of Uncertain Dynamical Systems
Abstract
Abstract. We consider risk-neutral optimal control problems governed by nonlinear ordinary differential equations with uncertain inputs. Using sample average approximation, we obtain optimal control problems with ensembles of deterministic dynamical systems. Leveraging techniques for metric entropy bounds, we derive nonasymptotic Monte Carlo–type convergence rates for the ensemble-based optimal values and critical points. Our theoretical framework is validated through numerical simulations on a harmonic oscillator problem and a vaccination scheduling problem for epidemic control under model parameter uncertainty.
Fields of Study & Subjects
Optimization and Variational Analysis
Publication details
- Journal / source
- SIAM Journal on Control and Optimization
- Volume
- 64
- Issue
- 3
- Pages
- 1631–1650
- Publication date
- 1 June 2026
- Language
- EN