Convergence rates for ensemble-based solutions to optimal control of uncertain dynamical systems
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866908808506245120 |
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| author | Melnikov, Olena Milz, Johannes |
| author_facet | Melnikov, Olena Milz, Johannes |
| contents | We consider optimal control problems involving nonlinear ordinary differential equations with uncertain inputs. Using the sample average approximation, we obtain optimal control problems with ensembles of deterministic dynamical systems. Leveraging techniques for metric entropy bounds, we derive non-asymptotic Monte Carlo-type convergence rates for the ensemble-based solutions. 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_18182 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Convergence rates for ensemble-based solutions to optimal control of uncertain dynamical systems Melnikov, Olena Milz, Johannes Optimization and Control 90C15, 90C30, 49K45, 49N60 We consider optimal control problems involving nonlinear ordinary differential equations with uncertain inputs. Using the sample average approximation, we obtain optimal control problems with ensembles of deterministic dynamical systems. Leveraging techniques for metric entropy bounds, we derive non-asymptotic Monte Carlo-type convergence rates for the ensemble-based solutions. 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. |
| title | Convergence rates for ensemble-based solutions to optimal control of uncertain dynamical systems |
| topic | Optimization and Control 90C15, 90C30, 49K45, 49N60 |
| url | https://arxiv.org/abs/2407.18182 |