Abstract
Under general hypotheses on the target set S and the dynamics of the system, we show that the minimal time function TS(·) is a proximal solution to the Hamilton-Jacobi equation. Uniqueness results are obtained with two different kinds of boundary conditions. A new propagation result is proven, and as an application, we give necessary and sufficient conditions for TS(·) to be Lipschitz continuous near S. A Petrov-type modulus condition is also shown to be sufficient for continuity of TS(·) near S.
Original language | English |
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Pages (from-to) | 1048-1072 |
Number of pages | 25 |
Journal | SIAM Journal on Control and Optimization |
Volume | 36 |
Issue number | 3 |
DOIs | |
State | Published - 1998 |
Keywords
- Continuity of value functions
- Hamilton-Jacobi equations
- Minimal time function
- Nonsmooth analysis
- Proximal analysis