Sugradient Formulas for Optimal Control Problems with Constant Dynamics

• Main Author: Huang, Lingyan
• Other Authors: Wolenski, Peter
• Format: Others
• Language: en
• Published: LSU 2012
• Subjects: Mathematics
• Online Access: http://etd.lsu.edu/docs/available/etd-11142012-144831/

In this thesis our first concern is the study of the minimal time function corresponding to control problems with constant convex dynamics and closed target sets. Unlike previous work in this area, we do not make any nonempty interior or calmness assumptions and the minimal time functions is generally non-Lipschitzian. We show that the Proximal and Fréchet subgradients of the minimal time function are computed in terms of normal vectors to level sets. And we also computed the subgradients of the minimal time function in terms of the F-projection. Secondly, we consider the value function for Bolza Problem in optimal control and the calculus of variations. The main results present refined formulas for calculating the Fréchet subgradient of the value function under minimal requirements, and are similar to those obtained for the minimal time function.