A Deterministic Approach To Stochastic Optimal Control With Application To Anticipative Control
A Deterministic Approach To Stochastic Optimal Control With Application To Anticipative Control
复制标题
随机最优控制的确定性方法及其在预期控制中的应用
DOI：
10.1080/17442509208833790
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发表时间：
1992
期刊：
影响因子：
--
通讯作者：
G. Burstein
中科院分区：
文献类型：
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作者：
Mark H.A.Davis;G. Burstein
利用SDE解的分解，我们将具有预期控制的随机最优控制问题视为一类由驱动Wiener过程和新引入的拉格朗日乘子随机过程（非预期性等式约束）的路径参数化的确定性控制问题。证明了这些问题的值函数是线性后向Hamilton-Jacobi-Bellman随机偏微分方程（HJB SPDE）的鲁棒方程（随机偏微分方程）的唯一全局解。当使用维纳过程的线性插值近似时，这表现为随机HJB PDE序列的极限SPDE。我们的方法通过展示它如何作为确定性动态规划方程序列的极限的平均值而出现，将SDE的Wong-Zakai型结果[20]扩展到随机动态规划方程。采用Kunita[13]的随机特征方法来表示。
Using the decomposition of solution of SDE, we consider the stochastic optimal control problem with anticipative controls as a family of deterministic control problems parametrized by the paths of the driving Wiener process and of a newly introduced Lagrange multiplier stochastic process (nonanticipativity equality constraint). It is shown that the value function of these problems is the unique global solution of a robust equation (random partial differential equation) associated to a linear backward Hamilton-Jacobi-Bellman stochastic partial differential equation (HJB SPDE). This appears as limiting SPDE for a sequence of random HJB PDE's when linear interpolation approximation of the Wiener process is used. Our approach extends the Wong-Zakai type results [20] from SDE to the stochastic dynamic programming equation by showing how this arises as average of the limit of a sequence of deterministic dynamic programming equations. The stochastic characteristics method of Kunita [13] is used to represent the ...