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 ε, the parameter of the approximation, goes to zero. First, for a twofold junction problem we characterize the limit value function as a 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 a maximal subsolution.

Hybrid Thermostatic Approximations of Junctions for Some Optimal Control Problems on Networks

Rosario Maggistro
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 ε, the parameter of the approximation, goes to zero. First, for a twofold junction problem we characterize the limit value function as a 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 a maximal subsolution.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10278/3716128
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