As its dual, observability, the controllability of controllable systems actuated in different ways can be quantified by coefficients which can be computed either by a numerical approach or a symbolic one. If the interpretation of observability coefficients is rather straightforward, this is not the case for controllability. This paper, after proposing slight but important adjustments to the computation of numerical controllability coefficients puts forward a numerical framework that can be used to provide some clue as how to interpret the role played by numerical and symbolical controllability coefficients. Using four different chaotic systems, it is showed how controllability may depend on the derivative to which the control law is applied and how this may be related to the corresponding coefficients. In practice could help to decide where to place actuators. The developed framework has two backbones: the power needed to achieve control and the rate of success of the control, the latter is not considered in the surveyed literature. Our results show that numerical and symbolic coefficients quantify different aspects of the problem and confirm how controllability is difficult to interpret in practice without any consideration for observability.

作为其双重可观察性，以不同方式驱动的可控系统的可控性可以通过系数进行量化，这些系数可以通过数值方法或符号方法计算。如果可观察性系数的解释相当简单，那么可控性就不是这样了。本文在对数值可控性系数的计算提出轻微但重要的调整后，提出了一个数值框架，可以用来为如何解释数值和符号可控性系数所起的作用提供一些线索。使用四种不同的混沌系统，展示了可控性如何取决于应用控制律的导数，以及这如何与相应的系数相关。在实践中可以帮助决定在哪里放置执行器。开发的框架有两个支柱：实现控制所需的功率和控制的成功率，后者在所调查的文献中没有考虑。我们的结果表明，数值和符号系数量化了问题的不同方面，并证实了在不考虑可观察性的情况下，在实践中如何难以解释可控性。