On the Connection between the Hamilton-Jacobi-Bellman and the Fokker-Planck Control Frameworks

On the Connection between the Hamilton-Jacobi-Bellman and the Fokker-Planck Control Frameworks

Annunziato, M. , Borzì, A. , Nobile, F. and Tempone, R., On the Connection between the Hamilton-Jacobi-Bellman and the Fokker-Planck Control Frameworks. Applied Mathematics, Vol.5 No.16, September 2014. DOI: 10.4236/am.2014.516239
Annunziato, M., Borzì, A., Nobile, F. and Tempone, R.
Hamilton-Jacobi-Bellman Equation, Fokker-Planck Equation, Optimal Control Theory, Stochastic Differential Equations, Hybrid Systems
2014
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.
ISSN Print: 2152-7385 ISSN Online: 2152-7393