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

Mario Annunziato, Alfio Borzì, Fabio Nobile, Raul Tempone

Research output: Contribution to journalArticlepeer-review

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 FokkerPlanck formalism allows considering a larger class of objectives. To illustrate the connection between the two control strategies, the cases of an Itō stochastic process and of a piecewise-deterministic process are considered.
Original languageEnglish (US)
Pages (from-to)2476-2484
Number of pages9
JournalApplied Mathematics
Volume05
Issue number16
DOIs
StatePublished - Sep 2 2014

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