In least costly experiment design, the optimal spectrum of an identification experiment is determined in such a way that the cost of the experiment is minimized under some accuracy constraint on the identified parameter vector. Like all optimal experiment design problems, this optimization problem depends on the unknown true system, which is generally replaced by an initial estimate. One important consequence of this is that we can underestimate the actual cost of the experiment and that the accuracy of the identified model can be lower than desired. Here, based on an a-priori uncertainty set for the true system, we propose a convex optimization approach that allows to prevent these issues from happening. We do this when the to-be-determined spectrum is the one of a multisine signal.

在最不昂贵的实验设计中，以某种方式确定识别实验的最佳光谱，以便在对识别出的参数向量进行一定精度约束的情况下，将实验成本降至最低。像所有最佳实验设计问题一样，此优化问题取决于未知的真实系统，该系统通常由初始估计值代替。这样做的一个重要后果是，我们可能会低估实验的实际成本，并且所识别模型的准确性可能会低于期望值。在此，基于为真实系统设置的先验不确定性，我们提出了一种凸优化方法，可以防止这些问题的发生。当待确定的频谱是多正弦信号之一时，我们将执行此操作。