On the minimum principle and dynamic programming for hybrid systems with low dimensional switching manifolds

A class of hybrid systems with both autonomous and controlled switchings and jumps is considered where switching manifolds corresponding to autonomous switchings and jumps are allowed to be codimension k submanifolds in ℝn with 1≤k≤n. Optimal control problems associated to this class of hybrid systems are studied where in addition to running and terminal costs, costs associated to switching between discrete states are allowed. Statements of the Hybrid Minimum Principle and Hybrid Dynamic Programming as well as their relationship are presented in this general setting and an illustrative example is provided.