Sampling in control applications is increasingly done non-equidistantly in time. This includes applications in motion control, networked control, resource-aware control, and event-based control. Some of these applications, like the ones where displacement is tracked using incremental encoders, are driven by signals that are only measured when their values cross fixed thresholds in the amplitude domain. This paper introduces a non-parametric estimator of the impulse response and transfer function of continuous-time systems based on such amplitude-equidistant sampling strategy, known as Lebesgue sampling. To this end, kernel methods are developed to formulate an algorithm that adequately takes into account the bounded output uncertainty between the event timestamps, which ultimately leads to more accurate models and more efficient output sampling compared to the equidistantly-sampled kernel-based approach. The efficacy of our proposed method is demonstrated through a mass–spring damper example with encoder measurements and extensive Monte Carlo simulation studies on system benchmarks.

中文翻译：

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使用勒贝格采样数据进行基于内核的识别

控制应用中的采样越来越多地以非等距方式及时完成。这包括运动控制、网络控制、资源感知控制和基于事件的控制中的应用。其中一些应用（例如使用增量编码器跟踪位移的应用）由仅当其值跨越幅度域中的固定阈值时才测量的信号驱动。本文介绍了一种基于这种幅度等距采样策略的连续时间系统的脉冲响应和传递函数的非参数估计器，称为勒贝格采样。为此，开发了核方法来制定一种算法，该算法充分考虑了事件时间戳之间的有界输出不确定性，与基于等距采样的核的方法相比，最终导致更准确的模型和更有效的输出采样。我们提出的方法的有效性通过带有编码器测量的质量弹簧阻尼器示例以及对系统基准的广泛蒙特卡洛模拟研究来证明。