State-constrained optimal control of the continuity equation and infinite-dimensional viscosity solutions
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866917380113825792 |
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| author | Bagagiolo, Fabio Romanò, Ivan |
| author_facet | Bagagiolo, Fabio Romanò, Ivan |
| contents | We study a finite horizon optimal control problem for the continuity equation under a weighted integral state constraint on the mass outside a fixed set. The model is cast in a Hilbert framework for densities. On a suitable invariant compact subset, we prove that the value function is Lipschitz continuous and satisfies, by dynamic programming, the associated infinite dimensional constrained Hamilton Jacobi Bellman equation in viscosity sense (subsolution in the interior, supersolution up to the boundary). We finally prove a comparison principle and uniqueness in the Lipschitz class. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_01768 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | State-constrained optimal control of the continuity equation and infinite-dimensional viscosity solutions Bagagiolo, Fabio Romanò, Ivan Optimization and Control 49L25 (Primary) 35R15, 49L20, 35L03, 35F21 (Secondary) We study a finite horizon optimal control problem for the continuity equation under a weighted integral state constraint on the mass outside a fixed set. The model is cast in a Hilbert framework for densities. On a suitable invariant compact subset, we prove that the value function is Lipschitz continuous and satisfies, by dynamic programming, the associated infinite dimensional constrained Hamilton Jacobi Bellman equation in viscosity sense (subsolution in the interior, supersolution up to the boundary). We finally prove a comparison principle and uniqueness in the Lipschitz class. |
| title | State-constrained optimal control of the continuity equation and infinite-dimensional viscosity solutions |
| topic | Optimization and Control 49L25 (Primary) 35R15, 49L20, 35L03, 35F21 (Secondary) |
| url | https://arxiv.org/abs/2604.01768 |