We study some optimal control problems on networks with junctions, approximate the junctions by a switching rule of delay-relay type and study the passage to the limit when the parameter of the approximation goes to zero. First, for a twofold junction problem we characterize the limit value function as viscosity solution and maximal subsolution of a suitable Hamilton-Jacobi problem. Then, for a threefold junction problem we consider two different approximations, recovering in both cases some uniqueness results in the sense of maximal subsolution.

Hybrid thermostatic approximations of junctions for some optimal control problems on networks / Bagagiolo, Fabio; Maggistro, Rosario. - In: SIAM JOURNAL ON CONTROL AND OPTIMIZATION. - ISSN 1095-7138. - ELETTRONICO. - 57:4(2019), pp. 2415-2442. [10.1137/17M111907X]

Hybrid thermostatic approximations of junctions for some optimal control problems on networks

Bagagiolo, Fabio;Maggistro, Rosario
2019-01-01

Abstract

We study some optimal control problems on networks with junctions, approximate the junctions by a switching rule of delay-relay type and study the passage to the limit when the parameter of the approximation goes to zero. First, for a twofold junction problem we characterize the limit value function as viscosity solution and maximal subsolution of a suitable Hamilton-Jacobi problem. Then, for a threefold junction problem we consider two different approximations, recovering in both cases some uniqueness results in the sense of maximal subsolution.
2019
4
Bagagiolo, Fabio; Maggistro, Rosario
Hybrid thermostatic approximations of junctions for some optimal control problems on networks / Bagagiolo, Fabio; Maggistro, Rosario. - In: SIAM JOURNAL ON CONTROL AND OPTIMIZATION. - ISSN 1095-7138. - ELETTRONICO. - 57:4(2019), pp. 2415-2442. [10.1137/17M111907X]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/236298
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