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

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DOI: 10.4236/am.2014.516239    2,782 Downloads   3,375 Views   Citations

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.

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Annunziato, M. , Borzì, A. , Nobile, F. and Tempone, R. (2014) On the Connection between the Hamilton-Jacobi-Bellman and the Fokker-Planck Control Frameworks. Applied Mathematics, 5, 2476-2484. doi: 10.4236/am.2014.516239.

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