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 illustrate the connection between the two control strategies, the cases of an Itō stochastic process and of a piecewise-deterministic process are considered.

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

ANNUNZIATO, Mario;
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 illustrate the 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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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11386/4479657
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