Abstract
We present several formulae for the proximal and Fréchet subdifferentials of the minimal time function defined by a linear control system and a target set. At every point inside the target set, the proximal/Fréchet subdifferential is the intersection of the proximal/Fréchet normal cone of the target set and an upper level set of a so-called Hamiltonian function which depends only on the linear control system. At every point outside the target set, under a mild assumption, proximal/Fréchet subdifferential is the intersection of the proximal/Fréchet normal cone of an enlargement of the target set and a level set of the Hamiltonian function.
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Jiang, Y., He, Y.R. & Sun, J. Subdifferential properties of the minimal time function of linear control systems. J Glob Optim 51, 395–412 (2011). https://doi.org/10.1007/s10898-010-9633-6
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DOI: https://doi.org/10.1007/s10898-010-9633-6