Advanced Computational Stochastic Dynamic Programming for Continuous Time Problems

本研究的目的是开发快速算法， 一般连续时间最优反馈控制 随机动力系统 这些随机动力系统 包括高斯和泊松白色噪声扰动。 最优反馈控制的计算处理 一般非线性随机微分方程 连续时间中的噪声，包括泊松噪声，是一种 这个项目的独特之处。 算法是 正在多状态资源模型上进行测试，但适用于 应用范围广泛。 数值方法 直接处理随机偏微分方程， 动态规划 新的数据结构和算法，例如 有限元和多重网格方法，将被开发， 减轻了对存储器和计算密集型的需求， “维度灾难” 目前， 为可扩展、大规模并行处理器和大规模 记忆超级计算机 结果给出了最优反馈控制 变量和预期的最佳性能指标， 状态变量和时间。 大规模科学计算是 对于管理计算和内存需求至关重要 大型应用的最优控制，如航空航天 动力学、柔性结构、资源、经济学和机器人技术。 先进的计算技术的实施，如 并行化、向量化和优化数据结构， 可以解决更大尺寸的问题。

The objective of this research is to develop fast algorithms for the optimal feedback control of general continuous time stochastic dynamical systems. These stochastic dynamical systems include perturbations by both Gaussian and Poisson white noise. The computational treatment of the optimal feedback control of general, nonlinear, stochastic differential equations with Markov noise in continuous time, including Poisson noise, is a particularly unique feature of this project. The algorithms are being tested on multi-state resource models, but are applicable to a wide variety of applications. The numerical approach directly treats the partial differential equation of stochastic dynamic programming. New data structures and algorithms, such as finite element and multigrid methods, will be developed to alleviate both memory and computation intensive demands from the "curse of dimensionality". Purely parallel methods are being developed for scalable, massively parallel processors and massive memory supercomputers. Results give the optimal feedback control variables and the expected optimal performance index in terms of state variables and time. Large scale scientific computing is essential for managing the computational and memory demands in the optimal control of large applications, such as aerospace dynamics, flexible structures, resources, economics and robotics. The implementation of advanced computational techniques, such as parallelization, vectorization and optimal data structures, make it possible to solve problems of larger dimension.