TITLE:
On the Connection between the Hamilton-Jacobi-Bellman and the Fokker-Planck Control Frameworks
AUTHORS:
Mario Annunziato, Alfio Borzì, Fabio Nobile, Raul Tempone
KEYWORDS:
Hamilton-Jacobi-Bellman Equation, Fokker-Planck Equation, Optimal Control Theory, Stochastic Differential Equations, Hybrid Systems
JOURNAL NAME:
Applied Mathematics,
Vol.5 No.16,
September
2,
2014
ABSTRACT: In the framework of
stochastic processes, the connection between the dynamic programming scheme
given by the Hamilton-Jacobi-Bellman equation and a recently proposed control
approach based on the Fokker-Planck equation is discussed. Under appropriate
assumptions it is shown that the two strategies are equivalent in the case of
expected cost functionals, while the Fokker-Planck formalism allows considering
a larger classof objectives. To illustratethe connection between the two
control strategies, the cases of an Itō stochastic process and of a
piecewise-deterministic process are considered.