论文标题
分配不确定性下离散时间随机最佳控制问题的最大原理
Maximum principle for discrete-time stochastic optimal control problem under distribution uncertainty
论文作者
论文摘要
在本文中，我们研究了凸控制域的分布不确定性下的离散时间随机最佳控制问题。通过弱收敛方法和Sion的最小定理，我们在参考概率$ p^{\ ast} $下获得了成本功能的变异不等式。此外，在噪声和控制的平方集成性条件下，我们在$ p^{\ ast} $下建立离散的随机最大原理。最后，我们引入了一种向后算法来计算参考概率$ p^{\ ast} $和最佳控制$ u^{\ ast} $。
In this paper, we study a discrete-time stochastic optimal control problem under distribution uncertainty with convex control domain. By weak convergence method and Sion's minimax theorem, we obtain the variational inequality for cost functional under a reference probability $P^{\ast}$. Moreover, under the square integrability condition for noise and control, we establish the discrete-time stochastic maximum principle under $P^{\ast}$. Finally, we introduce a backward algorithm to calculate the reference probability $P^{\ast}$ and the optimal control $u^{\ast}$.
