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Linear‐Quadratic Optimal Control Problem for Partially Observed Forward‐Backward Stochastic Differential Equations of Mean‐Field Type
Author(s) -
Ma Heping,
Liu Bin
Publication year - 2016
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.1310
Subject(s) - mathematics , optimal control , stochastic differential equation , decoupling (probability) , linear quadratic regulator , stochastic control , linear quadratic gaussian control , riccati equation , type (biology) , mathematical optimization , differential equation , mathematical analysis , ecology , control engineering , engineering , biology
This paper is concerned with the linear‐quadratic optimal control problem for partially observed forward‐backward stochastic differential equations (FBSDEs) of mean‐field type. Based on the classical spike variational method, backward separation approach as well as filtering technique, we first derive the necessary and sufficient conditions of the optimal control problem with the non‐convex domain. Nextly, by means of the decoupling technique, we obtain two Riccati equations, which are uniquely solvable under certain conditions. Also, the optimal cost functional is represented by the solutions of the Riccati equations for the special case.