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.File in questo prodotto:
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