FORWARD-BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS, LINEAR QUADRATIC STOCHASTIC OPTIMAL CONTROL AND NONZERO SUM DIFFERENTIAL GAMES
FORWARD-BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS, LINEAR QUADRATIC STOCHASTIC OPTIMAL CONTROL AND NONZERO SUM DIFFERENTIAL GAMES
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发表时间：
2005
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通讯作者：
Wu Zhen
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作者：
Wu Zhen
本文利用正倒向随机微分方程的解，得到了线性二次型随机最优控制问题的最优控制的显式形式和非零和微分对策问题的开环Nash平衡点。我们还讨论了广义Riccati方程组的可解性，并利用这类Riccati方程组的解给出了最优控制问题的线性反馈调节器。
In this paper, we use the solutions of forward-backward stochastic differential equations to get the explicit form of the optimal control for linear quadratic stochastic optimal control problem and the open-loop Nash equilibrium point for nonzero sum differential games problem. We also discuss the solvability of the generalized Riccati equation system and give the linear feedback regulator for the optimal control problem using the solution of this kind of Riccati equation system.