arXiv 1012.20922010-12-15math.OC

大规模随机最优控制中的价格分解

Price decomposition in large-scale stochastic optimal control

Kengy Barty, Pierre Carpentier, Guy Cohen, Pierre Girardeau

摘要：

我们感兴趣的是最优驱动的动力系统，可以由外源噪声的影响。这通常被称为随机最优控制（SOC）问题，而动态规划（DP）原理是解决它的自然方法。不幸的是，DP面临所谓的维数灾难：求解DP方程的复杂性随着足以做出最优决策的信息变量（状态变量）的维数呈指数增长。对于一类大的SOC问题，其中包括重要的实际问题，我们提出了一个原始的方式获得的策略来驱动系统。我们介绍的算法是基于拉格朗日松弛，其中的应用程序分解是众所周知的确定性框架。然而，它的应用程序，这样的闭环问题是不简单的，需要一个额外的统计近似的对偶过程。本文给出了一个收敛性证明，它直接来自于最优化中对偶问题的经典结果，并扩大了我们的近似所造成的误差。数值结果也提供了一个大规模的SOC问题。这个想法扩展了Barty，Carpentier和Girardeau（2010）提出的原始DADP算法。

英文摘要：

We are interested in optimally driving a dynamical system that can be influenced by exogenous noises. This is generally called a Stochastic Optimal Control (SOC) problem and the Dynamic Programming (DP) principle is the natural way of solving it. Unfortunately, DP faces the so-called curse of dimensionality: the complexity of solving DP equations grows exponentially with the dimension of the information variable that is sufficient to take optimal decisions (the state variable). For a large class of SOC problems, which includes important practical problems, we propose an original way of obtaining strategies to drive the system. The algorithm we introduce is based on Lagrangian relaxation, of which the application to decomposition is well-known in the deterministic framework. However, its application to such closed-loop problems is not straightforward and an additional statistical approximation concerning the dual process is needed. We give a convergence proof, that derives directly from classical results concerning duality in optimization, and enlghten the error made by our approximation. Numerical results are also provided, on a large-scale SOC problem. This idea extends the original DADP algorithm that was presented by Barty, Carpentier and Girardeau (2010).

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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