Turnpike and dissipativity in generalized discrete-time stochastic linear-quadratic optimal control
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866908382158389248 |
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| author | Schießl, Jonas Ou, Ruchuan Faulwasser, Timm Baumann, Michael Heinrich Grüne, Lars |
| author_facet | Schießl, Jonas Ou, Ruchuan Faulwasser, Timm Baumann, Michael Heinrich Grüne, Lars |
| contents | We investigate different turnpike phenomena of generalized discrete-time stochastic linear-quadratic optimal control problems. Our analysis is based on a novel strict dissipativity notion for such problems, in which a stationary stochastic process replaces the optimal steady state of the deterministic setting. We show that from this time-varying dissipativity notion, we can conclude turnpike behaviors concerning different objects like distributions, moments, or sample paths of the stochastic system and that the distributions of the stationary pair can be characterized by a stationary optimization problem. The analytical findings are illustrated by numerical simulations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_05422 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Turnpike and dissipativity in generalized discrete-time stochastic linear-quadratic optimal control Schießl, Jonas Ou, Ruchuan Faulwasser, Timm Baumann, Michael Heinrich Grüne, Lars Optimization and Control 93E20, 49N10, 93E15 We investigate different turnpike phenomena of generalized discrete-time stochastic linear-quadratic optimal control problems. Our analysis is based on a novel strict dissipativity notion for such problems, in which a stationary stochastic process replaces the optimal steady state of the deterministic setting. We show that from this time-varying dissipativity notion, we can conclude turnpike behaviors concerning different objects like distributions, moments, or sample paths of the stochastic system and that the distributions of the stationary pair can be characterized by a stationary optimization problem. The analytical findings are illustrated by numerical simulations. |
| title | Turnpike and dissipativity in generalized discrete-time stochastic linear-quadratic optimal control |
| topic | Optimization and Control 93E20, 49N10, 93E15 |
| url | https://arxiv.org/abs/2309.05422 |