Willems et al. showed that all input-output trajectories of a discrete-time linear time-invariant system can be obtained using linear combinations of time shifts of a single, persistently exciting, input-output trajectory of that system. In this paper, we extend this result to the class of discrete-time single-input single-output flat nonlinear systems. We propose a data-based parametrization of all trajectories using only input-output data. Further, we use this parametrization to solve the data-based simulation and output-matching control problems for the unknown system without explicitly identifying a model. Finally, we illustrate the main results with numerical examples.

中文翻译：

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平面非线性系统基于数据的系统分析与控制

威廉姆斯等。结果表明，离散时间线性时不变系统的所有输入输出轨迹都可以使用该系统单个持续激励的输入输出轨迹的时移的线性组合来获得。在本文中，我们将此结果扩展到离散时间单输入单输出平面非线性系统的类别。我们建议仅使用输入输出数据对所有轨迹进行基于数据的参数化。此外，我们使用此参数化来解决未知系统的基于数据的仿真和输出匹配控制问题，而无需明确识别模型。最后，我们用数值示例说明了主要结果。