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Linear−quadratic optimal control and nonzero‐sum differential game of forward−backward stochastic system
Author(s) -
Yu Zhiyong
Publication year - 2012
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.406
Subject(s) - uniqueness , differential game , nash equilibrium , monotonic function , stochastic differential equation , mathematics , optimal control , differential (mechanical device) , equilibrium point , mathematical economics , quadratic equation , point (geometry) , mathematical optimization , differential equation , mathematical analysis , engineering , aerospace engineering , geometry
An existence and uniqueness result for one kind of forward–backward stochastic differential equations with double dimensions was obtained under some monotonicity conditions. Then this result was applied to the linear‐quadratic stochastic optimal control and nonzero‐sum differential game of forward–backward stochastic system. The explicit forms of the optimal control and the Nash equilibrium point are obtained respectively. We note that our method is effective in studying the uniqueness of Nash equilibrium point.Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society