Assessing non-convex value functions for the optimal control of stochastic differential equations

Results in Control and Optimization

João B.R. do Val¹  Elmer Lévano²  Alessandro N. Vargas³ 

[1] School of Electrical and Computer Engineering, University of Campinas, UNICAMP, 13083-852, Campinas, SP, Brazil;Universidad Nacional de Ingeniería, Facultad de Engeniería Eléctrica y Electrónica, Av. Túpac Amaru 210 Campus UNI Rímac 15333, Lima, Peru;Universidade Tecnológica Federal do Paraná, UTFPR, Av. Alberto Carazzai 1640, 86300-000 Cornelio Procópio-PR, Brazil;

关键词: Optimal control;    Stochastic ordering;    Stochastic differential equations;    Value function;   

DOI  :  

来源: DOAJ

【 摘 要 】

Solving the optimal control of stochastic differential equations (SDEs) using the dynamic programming method requires writing the problem in terms of the so-called value function. This paper presents conditions to assure that the value function is convex away from the origin, a concept that allows the value function be non-convex in a region close to the origin. In contrast, for regions away from the origin, the value function remains convex under some mild conditions. Stochastic ordering is used to prove this result. A numerical example illustrates the potential benefits of our approach.

【 授权许可】

Unknown