Parallel Algorithms for Large Scale Optimal Control Programs

目前，还没有一种并行算法可以在拥有大量处理器的计算机上高效地解决最优控制问题。这项研究将开发两种并行算法来解决大规模最优控制问题，这些问题预计在大量处理器的情况下是有效的。第一种算法，称为混合算法，是微分动态规划(DDP)和分阶段牛顿方法的组合，这两种方法都是串联的。混合并行算法主要用于无约束最优控制问题。第二种算法称为SQP型算法，它是利用最优控制问题的特点和序列二次规划(SQP)方法导出的。SQP型算法既适用于无约束最优控制问题，也适用于约束最优控制问题。在这两种算法中，每个处理器都被指派在一组时间段内解决一个优化问题。代码将被开发用于具有中粒度并行能力的机器，例如Intel iPSC/860和Kendall Square计算机。一个典型的工程应用涉及10,000个时间周期的非线性柔性结构问题，将被用来评估所提出的算法。

Currently, there is no parallel algorithm that can solve optimal control problems efficiently on computers with a large number of processors. This research will develop two parallel algorithms to solve large scale optimal control problems that are expected to be efficient with a large number of processors. The first algorithm, called the Hybrid algorithm, is a combination of the Differential Dynamic Programming (DDP) and a stagewise Newton's method, both of which are serial. The Hybrid parallel algorithm is designed primarily for unconstrained optimal control problems. The second algorithm, called an SQP-type algorithm, is derived by utilizing special features of the optimal control problem along with a Sequential Quadratic Programming (SQP) approach. The SQP-type algorithm is suitable for both the unconstrained and constrained optimal control problem. In both algorithms, each processor is assigned to solve an optimization problem over a group of time periods. Codes will be developed for machines with medium-grain parallel capabilities e.g., the Intel iPSC/860 and Kendall Square computers. A typical engineering application involving a nonlinear flexible structural problem with 10,000 time periods will be used to evaluate the proposed algorithms.