Continuous State Dynamic Programming Algorithms for Supercomputers

动态规划算法被广泛应用于非线性动态系统的控制分析。这些算法的计算量很大，特别是对于随机问题。超级计算机和并行处理将促进动态规划算法的使用，以解决过去由于计算限制而无法解决的现实问题。本文主要研究了随机动态规划（SDP）和微分动态规划（DDP）的并行处理，DDP与有限元模型的耦合，以及具有二元控制变量的SDP的特殊算法。研究重点是具有连续值状态变量的系统，因此分析将研究在状态空间中使用线性或非线性插值的SDP计算。将研究使用隐式或显式有限元模型结合DPP对CPU和并行处理的计算效果。大规模数值结果将在康奈尔国家超级计算机设施（CNSF）与CNSF工作人员合作计算。调查结果将应用于环境管理中出现的几个“实际”问题以及假想的测试实例。//

Dynamic programming algorithms are widely used for analyzing the control of nonlinear dynamic systems. These algorithms are computationally intensive, especially for stochastic problems. Supercomputers and parallel processing will facilitate the use of dynamic programming algorithms for realistic problems that could not be addressed in the past because of computational limitations. The proposal concentrates on the following issues: a) parallel processing of Stochastic Dynamic Programming (SDP) and Differential Dynamic Programming (DDP), b) coupling DDP to finite elements models, and c)special algorithms for SDP with binary control variables. The research focuses on systems with continuously valued state variables, and hence the analysis will examine the computation of SDP with linear or nonlinear interpolation in the state space. The computational effect on CPU and on parallel processing of using implicit or explicit finite element models in conjunction with DPP will be investigated. Large-scale numerical results will be computed at the Cornell National Supercomputer Facility (CNSF) in co-operation with CNSF staff. The results of the investigation will be applied to several "real" problems arising in environmental management as well as to hypothetical test examples.//