Stochastic optimization of a mixed moving average process for controlling non-Markovian streamflow environments
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866918211995303936 |
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| author | Yoshioka, Hidekazu Tanaka, Tomohiro Yoshioka, Yumi Hashiguchi, Ayumi |
| author_facet | Yoshioka, Hidekazu Tanaka, Tomohiro Yoshioka, Yumi Hashiguchi, Ayumi |
| contents | We investigated a cost-constrained static ergodic control problem of the variance of measure-valued affine processes and its application in streamflow management. The controlled system is a jump-driven mixed moving average process that generates realistic subexponential autocorrelation functions, and the static nature of the control originates from a realistic observability assumption in the system. The Markovian lift was effectively used to discretize the system into a finite-dimensional process, which is easier to analyze. The resolution of the problem is based on backward Kolmogorov equations and a quadratic solution ansatz. The control problem has a closed-form solution, and the variance has both strict upper and lower bounds, indicating that the variance cannot take an arbitrary value even when it is subject to a high control cost. The correspondence between the discretized system based on the Markovian lift and the original infinite-dimensional one is discussed. Then, a convergent Markovian lift is presented to approximate the infinite-dimensional system. Finally, the control problem was applied to real cases using available data for a river reach. An extended problem subject to an additional constraint on maintaining the flow variability was also analyzed without significantly degrading the tractability of the proposed framework. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_00747 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Stochastic optimization of a mixed moving average process for controlling non-Markovian streamflow environments Yoshioka, Hidekazu Tanaka, Tomohiro Yoshioka, Yumi Hashiguchi, Ayumi Optimization and Control Systems and Control We investigated a cost-constrained static ergodic control problem of the variance of measure-valued affine processes and its application in streamflow management. The controlled system is a jump-driven mixed moving average process that generates realistic subexponential autocorrelation functions, and the static nature of the control originates from a realistic observability assumption in the system. The Markovian lift was effectively used to discretize the system into a finite-dimensional process, which is easier to analyze. The resolution of the problem is based on backward Kolmogorov equations and a quadratic solution ansatz. The control problem has a closed-form solution, and the variance has both strict upper and lower bounds, indicating that the variance cannot take an arbitrary value even when it is subject to a high control cost. The correspondence between the discretized system based on the Markovian lift and the original infinite-dimensional one is discussed. Then, a convergent Markovian lift is presented to approximate the infinite-dimensional system. Finally, the control problem was applied to real cases using available data for a river reach. An extended problem subject to an additional constraint on maintaining the flow variability was also analyzed without significantly degrading the tractability of the proposed framework. |
| title | Stochastic optimization of a mixed moving average process for controlling non-Markovian streamflow environments |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2210.00747 |