Subdifferential properties of the minimal time function of linear control systems

Subdifferential properties of the minimal time function of linear control systems

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Article ID: iaor20119953
Volume: 51
Issue: 3
Start Page Number: 395
End Page Number: 412
Publication Date: Nov 2011
Journal: Journal of Global Optimization
Authors: , ,
Keywords: control, programming: linear, programming: multiple criteria
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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