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

• 作者: Alfio Borzì Fabio Nobile Mario Annunziato Raul Tempone
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: Hamilton-Jacobi-Bellman EQUATION FOKKER-PLANCK EQUATION Optimal CONTROL Theory STOCHASTIC DIFFERENTIAL EQUATIONS Hybrid Systems
• 年，卷（期）: yysxyw_2014,（16）
• 页码范围: 2476-2484
• 页数: 9页
• 分类号: O1

摘要

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.