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- W4229442968 abstract "In this article, a notion of viscosity solutions is introduced for first order path-dependent Hamilton–Jacobi–Bellman (PHJB) equations associated with optimal control problems for path-dependent evolution equations in Hilbert space. We identify the value functional of optimal control problems as unique viscosity solution to the associated PHJB equations without the assumption (A.4) on page 231 of Li and Yong (1995). We also show that our notion of viscosity solutions is consistent with the corresponding notion of classical solutions, and satisfies a stability property." @default.
- W4229442968 created "2022-05-11" @default.
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- W4229442968 date "2022-08-01" @default.
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- W4229442968 title "Viscosity solutions to first order path-dependent Hamilton–Jacobi–Bellman equations in Hilbert space" @default.
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- W4229442968 doi "https://doi.org/10.1016/j.automatica.2022.110347" @default.
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