On Certain Hypotheses in Optimal Control Theory and the Relationship of   the Maximum Principle with the Dynamic Programming Method Proposed by L. I.   Rozonoer
  In this paper we will study three hypotheses proposed by L. I. Rozonoer (Automation and Remote Control, 2003, vol.64, no.8, pp.1237--1240) in optimal control theory in order to derive conditions for the existence of an optimal control under all initial conditions, and the relationships between Pontryagin maximum principle and the dynamic programming method. 
Hanzhong Wu