Despite the existence of formal guarantees for learning-based control approaches, the relationship between data and control performance is still poorly understood. In this paper, we propose a Lyapunov-based measure for quantifying the impact of data on the certifiable control performance. By modeling unknown system dynamics through Gaussian processes, we can determine the interrelation between model uncertainty and satisfaction of stability conditions. This allows us to directly asses the impact of data on the provable stationary control performance, and thereby the value of the data for the closed-loop system performance. Our approach is applicable to a wide variety of unknown nonlinear systems that are to be controlled by a generic learning-based control law, and the results obtained in numerical simulations indicate the efficacy of the proposed measure.

翻译：尽管存在以学习为基础的控制方法的正式保障,但数据与控制性能之间的关系仍然没有得到很好的理解。在本文件中,我们建议采取以Lyapunov为基础的措施,量化数据对可验证的控制性能的影响。通过高山进程模拟未知的系统动态,我们可以确定模型不确定性和稳定性条件的满意度之间的相互关系。这使我们能够直接评估数据对可证实的固定性控制性能的影响,从而评估数据对闭路系统性能的价值。我们的方法适用于由通用学习控制法控制的多种未知的非线性系统,在数字模拟中获得的结果表明了拟议措施的效力。