On the hybrid dynamic programming principle

Summary form only given, as follows. A Class of the hybrid optimal 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. 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 (HDPPP) leads to a hybrid HJB equation.