Subdifferential properties of the minimal time function of linear control systems
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...
| Main Authors: | , , |
|---|---|
| Format: | Journal Article |
| Published: |
Springer
2011
|
| Online Access: | http://hdl.handle.net/20.500.11937/40464 |
| Summary: | 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. |
|---|