Weak epigraphical solutions to Hamilton-Jacobi-Bellman equations on infinite horizon

Autor: Vincenzo Basco

In this paper we show a uniqueness result for weak epigraphical solutions of Hamilton-Jacobi-Bellman (HJB) equations on infinite horizon for a class of lower semicontinuous functions vanishing at infinity. Weak epigraphical solutions of HJB equations

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::3fd1c5b4d61441ac837a0da1cdbbf5c1
http://arxiv.org/abs/2208.08720

The distance function in the presence of an obstacle

Autor: Paolo Albano, Vincenzo Basco, Piermarco Cannarsa

We study the Riemannian distance function from a fixed point (a point-wise target) of Euclidean space in the presence of a compact obstacle bounded by a smooth hypersurface. First, we show that such a function is locally semiconcave with a fractional

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6fb5d71b725cc48252d3f08b9ee84ce3
https://hdl.handle.net/11585/901222

Hamilton–Jacobi–Bellman Equations with Time-Measurable Data and Infinite Horizon

Autor: Hélène Frankowska, Vincenzo Basco

Publikováno v: Nonlinear Differential Equations and Applications
Nonlinear Differential Equations and Applications, Springer Verlag, 2019, 26 (1), ⟨10.1007/s00030-019-0553-y⟩
Nonlinear Differential Equations and Applications, Springer Verlag, 2019, 26 (7), ⟨10.1007/s00030-019-0553-y⟩

In this paper we investigate the existence and uniqueness of weak solutions of the nonautonomous Hamilton–Jacobi–Bellman equation on the domain $$(0,\infty ) \times \Omega $$ . The Hamiltonian is assumed to be merely measurable in time variable a

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8c873a68308d9eb5cc4c48165e98ec70
https://hal.archives-ouvertes.fr/hal-02126128

Lipschitz Continuity of the Value Function for the Infinite Horizon Optimal Control Problem Under State Constraints

Autor: Hélène Frankowska, Vincenzo Basco

Publikováno v: Trends in Control Theory and Partial Differential Equations ISBN: 9783030179489
Trends in Control Theory and Partial Differential Equations, Springer INDAM series, 32, Springer Verlag, 17-38
Trends in Control Theory and Partial Differential Equations, Springer INDAM series, 32, Springer Verlag, 17-38, 2019, ⟨10.1007/978-3-030-17949-6_2⟩

International audience; This paper investigates sufficient conditions for Lipschitz regularity of the value function for an infinite horizon optimal control problem subject to state constraints. We focus on problems with a cost functional that includ

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2c6fa53cd61e88f792631baf9b23cb4c
https://doi.org/10.1007/978-3-030-17949-6_2

Necessary conditions for infinite horizon optimal control problems with state constraints

Autor: Piermarco Cannarsa, Vincenzo Basco, Hélène Frankowska

Publikováno v: Mathematical Control and Related Fields
Mathematical Control and Related Fields, AIMS, 2018, 8 (3), pp.535-555. ⟨10.3934/mcrf.2018022⟩

International audience; Partial and full sensitivity relations are obtained for nonauto-nomous optimal control problems with infinite horizon subject to state constraints , assuming the associated value function to be locally Lipschitz in the state.

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ec18e685b55f4fc457e3303c5b311ad6
https://hal.archives-ouvertes.fr/hal-02126115