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首页> 外文期刊>Jahresbericht der Deutschen Mathematiker-Vereinigung >Preface Issue 1-2016
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Preface Issue 1-2016

机译：前言1-2016

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摘要

Keeping systems (almost) forever within a range of acceptable states at lowest possible costs is the objective of "infinite horizon optimal control". To really find and calculate an (almost) optimal control strategy is, however, most difficult and in many cases almost impossible. In order to do this, it would indeed be necessary to calculate the effect of possible controls for infinitely many time steps. In reality, decisions are made by thinking a couple of time steps ahead. This means that the strategy will be chosen by solving "finite horizon optimal control" problems. But thinking e.g. of public budgets, investment strategies of companies or of the maintenance of cars, houses or public infrastructure makes it obvious that the control strategy will in many cases sensitively depend on the chosen time horizon. Lars Grime addresses this question and explains in a very comprehensible way under which conditions solutions of "receding horizon optimal control" problems could serve as a reliable approximation for infinite horizon problems.
机译：将系统（几乎）以尽可能低的成本永远保持在可接受状态的范围内是“无限视界最佳控制”的目标。然而，真正找到并计算（几乎）最优控制策略是最困难的，在许多情况下几乎是不可能的。为此，确实有必要计算无限多个时间步长的可能控制的效果。实际上，决策是通过考虑几个时间步长来做出的。这意味着将通过解决“有限范围最优控制”问题来选择策略。但是思考从公共预算，公司的投资策略或汽车，房屋或公共基础设施的维护策略来看，很明显，控制策略在许多情况下将取决于所选的时间范围。拉尔斯·格莱姆（Lars Grime）解决了这个问题，并以一种非常容易理解的方式解释了在这种情况下，“后视最优控制”问题的条件解决方案可以用作无限视界问题的可靠近似。

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