论文标题
最佳控制中的收费公路属性：离散时间和连续时间结果的概述
Turnpike Properties in Optimal Control: An Overview of Discrete-Time and Continuous-Time Results
论文作者
论文摘要
收费公路属性是指在许多最佳控制问题中，针对不同初始条件的解决方案和各种视野的解决方案接近特定稳定状态的社区，然后在时间范围内留在这个社区，直到最终离开。尽管对现象的早期观察可以追溯到1928年和1938年关于经济学问题的拉姆西和冯·诺伊曼的作品，但自1960年代以来，收费公路财产对经济学产生了不断的兴趣，以及最近对系统和控制的兴趣。本章提供了有限和无限维度的离散时间和连续时间结果的介绍概述。我们评论基于消散性的方法和无限 - 马森的结果，这使收费公路的特性可以利用长长和无限范围的问题的数值解决方案。在借鉴数字示例之后，本章以时间变化，打折和开放问题的前景结束。
The turnpike property refers to the phenomenon that in many optimal control problems, the solutions for different initial conditions and varying horizons approach a neighborhood of a specific steady state, then stay in this neighborhood for the major part of the time horizon, until they may finally depart. While early observations of the phenomenon can be traced back to works of Ramsey and von Neumann on problems in economics in 1928 and 1938, the turnpike property received continuous interest in economics since the 1960s and recent interest in systems and control. The present chapter provides an introductory overview of discrete-time and continuous-time results in finite and infinite-dimensions. We comment on dissipativity-based approaches and infinite-horizon results, which enable the exploitation of turnpike properties for the numerical solution of problems with long and infinite horizons. After drawing upon numerical examples, the chapter concludes with an outlook on time-varying, discounted, and open problems.
