| FORWARD-BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS, LINEAR QUADRATIC STOCHASTIC OPTIMAL CONTROL AND NONZERO SUM DIFFERENTIAL GAMES |
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| 引用本文： | WUZhen. FORWARD-BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS, LINEAR QUADRATIC STOCHASTIC OPTIMAL CONTROL AND NONZERO SUM DIFFERENTIAL GAMES[J]. 系统科学与复杂性, 2005, 18(2): 179-192 |
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| 作者姓名： | WUZhen |
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| 作者单位： | SchoolofMathematicsandSystemsScience,ShandongUniversity,Jinan250100,China |
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| 基金项目： | This work is supported by the National Natural Science Foundation (Grant No.10371067)the Youth Teacher Foundation of Fok Ying Tung Education Foundation, the Excellent Young Teachers Program and the Doctoral Program Foundation of MOE and Shandong Province, China. |
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| 摘 要： | 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.
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| 关 键 词： | 微分方程 随机最佳控制 布朗运动 随机线性方程 |
FORWARD-BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS, LINEAR QUADRATIC STOCHASTIC OPTIMAL CONTROL AND NONZERO SUM DIFFERENTIAL GAMES |
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| WU Zhen. FORWARD-BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS, LINEAR QUADRATIC STOCHASTIC OPTIMAL CONTROL AND NONZERO SUM DIFFERENTIAL GAMES[J]. Journal of Systems Science and Complexity, 2005, 18(2): 179-192 |
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| Authors: | WU Zhen |
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| Abstract: | 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. |
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| Keywords: | Stochastic differential equations stochastic optimal control Riccati equation nonzero sum stochastic differential game. |
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