最优控制的科学基础：免费午餐的证据
Common Foundations of Optimal Control Across the Sciences: evidence of a free lunch
摘要：
科学中的一个共同目标是通过选择控制变量来优化目标函数，从而实现期望的结果。这种情况下，可以表示在一个控制景观的目标被认为是控制变量的函数。在最基本的层面上，众所周知，绝大多数量子控制景观都没有陷阱，陷阱的存在会阻碍实现目标。本文回顾并扩展了量子控制景观评估，提供证据表明许多其他科学领域也存在同样非常有利的景观特征。这一更广泛的证据的影响进行了讨论。具体而言，控制景观的例子，从量子力学，化学和进化生物学。尽管有明显的差异，这些领域之间的共同点是突出在一个统一的数学框架。这个数学框架是由广泛的实验证据驱动的，这些证据表明很容易找到最佳控制（就实验室设置开销之外所需的算法搜索工作而言）。这种观察到的共同控制行为的全部范围和影响提出了一个开放的问题，在进一步的工作中进行评估。
英文摘要：
A common goal in the sciences is optimization of an objective function by selecting control variables such that a desired outcome is achieved. This scenario can be expressed in terms of a control landscape of an objective considered as a function of the control variables. At the most basic level, it is known that the vast majority of quantum control landscapes possess no traps, whose presence would hinder reaching the objective. This paper reviews and extends the quantum control landscape assessment, presenting evidence that the same highly favorable landscape features exist in many other domains of science. The implications of this broader evidence are discussed. Specifically, control landscape examples from quantum mechanics, chemistry, and evolutionary biology are presented. Despite the obvious differences, commonalities between these areas are highlighted within a unified mathematical framework. This mathematical framework is driven by the wide ranging experimental evidence on the ease of finding optimal controls (in terms of the required algorithmic search effort beyond laboratory set up overhead). The full scope and implications of this observed common control behavior pose an open question for assessment in further work.
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