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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2309.08280 |
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| _version_ | 1866929322703454208 |
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| author | Herty, Michael Kouhkouh, Hicham |
| author_facet | Herty, Michael Kouhkouh, Hicham |
| contents | The control of relaxation-type systems of ordinary differential equations is investigated using the Hamilton-Jacobi-Bellman equation. First, we recast the model as a singularly perturbed dynamics which we embed in a family of controlled systems. Then we study this dynamics together with the value function of the associated optimal control problem. We provide an asymptotic expansion in the relaxation parameter of the value function. We also show that its solution converges toward the solution of a Hamilton-Jacobi-Bellman equation for a reduced control problem. Such systems are motivated by semi-discretisation of kinetic and hyperbolic partial differential equations. Several examples are presented including Jin-Xin relaxation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_08280 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Relaxation and asymptotic expansion of controlled stiff differential equations Herty, Michael Kouhkouh, Hicham Optimization and Control 34H05, 35F21 The control of relaxation-type systems of ordinary differential equations is investigated using the Hamilton-Jacobi-Bellman equation. First, we recast the model as a singularly perturbed dynamics which we embed in a family of controlled systems. Then we study this dynamics together with the value function of the associated optimal control problem. We provide an asymptotic expansion in the relaxation parameter of the value function. We also show that its solution converges toward the solution of a Hamilton-Jacobi-Bellman equation for a reduced control problem. Such systems are motivated by semi-discretisation of kinetic and hyperbolic partial differential equations. Several examples are presented including Jin-Xin relaxation. |
| title | Relaxation and asymptotic expansion of controlled stiff differential equations |
| topic | Optimization and Control 34H05, 35F21 |
| url | https://arxiv.org/abs/2309.08280 |