Learning models or control policies from data has become a powerful tool to improve the performance of uncertain systems. While a strong focus has been placed on increasing the amount and quality of data to improve performance, data can never fully eliminate uncertainty, making feedback necessary to ensure stability and performance. We show that the control frequency at which the input is recalculated is a crucial design parameter, yet it has hardly been considered before. We address this gap by combining probabilistic model learning and sampled-data control. We use Gaussian processes (GPs) to learn a continuous-time model and compute a corresponding discrete-time controller. The result is an uncertain sampled-data control system, for which we derive robust stability conditions. We formulate semidefinite programs to compute the minimum control frequency required for stability and to optimize performance. As a result, our approach enables us to study the effect of both control frequency and data on stability and closed-loop performance. We show in numerical simulations of a quadrotor that performance can be improved by increasing either the amount of data or the control frequency, and that we can trade off one for the other. For example, by increasing the control frequency by 33%, we can reduce the number of data points by half while still achieving similar performance.

翻译：从数据中学习模型或控制策略已成为提升不确定系统性能的强大工具。尽管人们高度重视通过增加数据量和提升数据质量来改善性能，但数据永远无法完全消除不确定性，因此必须借助反馈来确保稳定性和性能。我们证明，计算输入时的控制频率是一个关键的设计参数，然而此前几乎未被考虑过。我们通过结合概率模型学习与采样数据控制来填补这一空白。我们利用高斯过程（GPs）学习连续时间模型，并计算相应的离散时间控制器。最终得到一个不确定的采样数据控制系统，并为其推导出鲁棒稳定性条件。我们构建半定规划来计算维持稳定性所需的最小控制频率，并优化性能。由此，我们的方法能够研究控制频率和数据对稳定性及闭环性能的影响。在四旋翼飞行器的数值仿真中，我们发现：增加数据量或提高控制频率均可提升性能，且两者之间可以相互权衡。例如，将控制频率提高33%，可在实现相似性能的同时将数据点数量减半。