Open AccessOptimal control of backward doubly stochastic system
Author(s) -
Wang Wencan
Publication year - 2019
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2018.6249
Subject(s) - optimal control , mathematics , stochastic differential equation , stochastic control , maximum principle , duality (order theory) , constraint (computer aided design) , adjoint equation , control theory (sociology) , mathematical optimization , domain (mathematical analysis) , state (computer science) , differential equation , control (management) , mathematical analysis , computer science , algorithm , geometry , discrete mathematics , artificial intelligence
An optimal control problem for backward doubly stochastic system is considered, where the control domain is not necessarily convex. By the method of classical spike variation and duality technique, one necessary condition and one sufficient condition are established for this kind of optimal control problem. The related adjoint process is characterised by the solution of a forward doubly stochastic differential equation, which formulates a forward–backward doubly stochastic differential equation coupled with the state equation. As an illustration, the authors' theoretical results are applied to study an optimal harvesting problem and a linear‐quadratic optimal control problem. Moreover, the corresponding maximum principle with an initial state constraint is obtained by Ekeland's variational principle.