Limiting subgradients of minimal time functions in Banach spaces

摘要

The paper mostly concerns the study of generalized differential properties of the so-called minimal time functions associated, in particular, with constant dynamics and arbitrary closed target sets in control theory. Functions of this type play a significant role in many aspects of optimization, control theory, and Hamilton-Jacobi partial differential equations. We pay the main attention to computing and estimating limiting subgradients of the minimal value functions and to deriving the corresponding relations for Frechet type ￡-subgradients in arbitrary Banach spaces.