A Hamiltonian approach using partial differential equations for open-loop stochastic optimal control

This paper utilizes a minimum principle for in finite dimensional systems for the optimal control of systems constrained by the Fokker-Plank equation governing the evolution of a state probability density function. From the backwards evolution of the corresponding adjoint system, we define a Hamiltonian and use its gradient to construct a numerical optimal control. The basic nature of the adjoint system allows for all of the necessary terms defining the control to be inferred from stochastic process samples which is exploited in provided examples. Solving stochastic optimal control problems utilizing stochastic processes is a promising approach for solving open loop stochastic optimal control problems of non-linear dynamic systems with a multi-dimensional state vector.