论文标题
有限维最佳控制问题的算法指南
An algorithmic guide for finite-dimensional optimal control problems
论文作者
论文摘要
我们调查有限维非线性最佳控制的主要数值技术。本章是为希望快速熟悉用于有效解决最佳控制问题的主要数值方法的从业者的指南。我们考虑了两个经典的例子，简单但很重要，足以丰富并推广到其他环境：Zermelo和Goddard问题。我们提供用于求解它们的代码的示例，并在线提供这些代码。我们讨论了直接和间接的方法，汉密尔顿 - 雅各比的方法，以乐观的计划结束。这些示例说明了每种方法的利弊，我们展示了如何将这些方法合并为强大的工具，以用于用于普通微分方程的最佳控制问题的数值解决方案。
We survey the main numerical techniques for finite-dimensional nonlinear optimal control. The chapter is written as a guide to practitioners who wish to get rapidly acquainted with the main numerical methods used to efficiently solve an optimal control problem. We consider two classical examples, simple but significant enough to be enriched and generalized to other settings: Zermelo and Goddard problems. We provide sample of the codes used to solve them and make these codes available online. We discuss direct and indirect methods, Hamilton-Jacobi approach, ending with optimistic planning. The examples illustrate the pros and cons of each method, and we show how these approaches can be combined into powerful tools for the numerical solution of optimal control problems for ordinary differential equations.
