A maximum principle for hybrid optimal control problems with pathwise state constraints

This paper provides necessary conditions of optimality, in the form of a maximum principle, for a broad class of hybrid optimal control problems, in which the dynamics of the constituent processes take the form of differential equations with control terms, and restrictions on the transitions or switches between operating modes are described by collections of functional equality and inequality constraints. Different choices of the constraint functionals capture a wide range of possible autonomous and controlled switching strategies. A notable feature of our formulation is the provision it makes for pathwise state constraints on the continuous variables.