A verification theorem for hybrid optimal control problem

@article{Shaikh2009AVT,
  title={A verification theorem for hybrid optimal control problem},
  author={M. Shahid Shaikh and Peter E. Caines},
  journal={2009 IEEE 13th International Multitopic Conference},
  year={2009},
  pages={1-3}
}
A class of the hybrid optimal control problem is formulated and a hybrid dynamic programming principle (DPP) is presented which constitutes a generalization of the celebrated dynamic programming principle of Richard Bellman [1]. It is shown that similarly to the case of continuous dynamic programming, which leads to the well known Hamilton-Jacobi-Bellman (HJB) functional partial differential equation, the hybrid dynamic programming principle (HDPP) leads to a hybrid HJB equation.