Game-theoretic and risk-sensitive stochastic optimal control via forward and backward stochastic differential equations
Game-theoretic and risk-sensitive stochastic optimal control via forward and backward stochastic differential equations
复制标题
DOI：
10.1109/cdc.2016.7799215
复制
发表时间：
2016-12
期刊：
影响因子：
--
通讯作者：
Ioannis Exarchos;Evangelos A. Theodorou;P. Tsiotras
中科院分区：
文献类型：
--
作者：
Ioannis Exarchos;Evangelos A. Theodorou;P. Tsiotras
在这项工作中，我们提出了一种基于抽样的算法，用于解决博弈论控制问题和风险敏感随机最优控制问题。该方法的基础是用前向和后向随机微分方程(FBSDE)的形式来描述问题。借助于非线性形式的Feynman-Kac引理，我们得到了非线性Hamilton-Jacobi-Isaacs方程的解的概率表示，表示为一个解耦的FBSDE系统。然后，可以使用线性回归技术来模拟这个FBSDE系统。利用随机微分对策与风险敏感最优控制之间的联系，我们证明了该算法同样适用于后一类问题。仿真结果验证了该算法的有效性。
In this work we present a sampling-based algorithm designed to solve game-theoretic control problems and risk-sensitive stochastic optimal control problems. The cornerstone of the proposed approach is the formulation of the problem in terms of forward and backward stochastic differential equations (FBSDEs). By means of a nonlinear version of the Feynman-Kac lemma, we obtain a probabilistic representation of the solution to the nonlinear Hamilton-Jacobi-Isaacs equation, expressed in the form of a decoupled system of FBSDEs. This system of FBSDEs can then be simulated by employing linear regression techniques. Utilizing the connection between stochastic differential games and risk-sensitive optimal control, we demonstrate that the proposed algorithm is also applicable to the latter class of problems. Simulation results validate the algorithm.