Extended Applicability of the Symplectic Pontryagin Method
This is an incremental theoretical improvement for researchers using the Symplectic Pontryagin method in optimal control.
The paper extends the applicability of the Symplectic Pontryagin method by proving its convergence under less restrictive assumptions, removing the need for a bounded gradient of the discrete dual variable.
The Symplectic Pontryagin method was introduced in a previous paper. This work shows that this method is applicable under less restrictive assumptions. Existence of solutions to the Symplectic Pontryagin scheme are shown to exist without the previous assumption on a bounded gradient of the discrete dual variable. The convergence proof uses the representation of solutions to a Hamilton-Jacobi-Bellman equation as the value function of an associated variation problem.