Extended applications of generating functions to optimal feedback control problems

As a natural extension of our recent work on finding optimal feedback control laws based on generating functions of a Hamiltonian system, we consider an optimal control problem with control constraints and a singular optimal control problem. For the problem with control constraints, we consider the time optimal control of the double integrator, and show that our approach can recover the necessary and sufficient conditions of optimal feedback control laws directly. For the singular optimal control problem, we study the linear quadratic problem and show that our method reproduces the conventional solution satisfying the necessary conditions for optimality. The current study is used to more fully understand our approach with the goal of defining a method that is applicable to more general systems.