In this paper, we present a data-driven controller design method for continuous-time nonlinear systems with rational system dynamics, using no model knowledge but only measured data affected by noise. We first extend recent results on data-driven control for linear time-invariant systems by presenting a purely data-driven representation of unknown nonlinear systems with rational dynamics. By applying robust control techniques to this parametrization, we obtain sum-of-squares based criteria for designing controllers with closed-loop robust stability guarantees for all continuous-time systems with rational system dynamics which are consistent with the measured data and the assumed noise bound. Finally, we apply the developed approach to a numerical example.

中文翻译：

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具有理性动力学的非线性系统的数据驱动镇定

在本文中，我们提出了一种具有合理系统动力学的连续时间非线性系统的数据驱动控制器设计方法，该方法不使用任何模型知识，而仅使用受噪声影响的测量数据。我们首先通过提供具有动力学原理的未知非线性系统的纯数据驱动表示，来扩展线性时不变系统的数据驱动控制的最新结果。通过将鲁棒控制技术应用于此参数化，我们获得了基于平方和的标准，用于为具有合理系统动力学的所有连续时间系统设计闭环鲁棒稳定性保证的控制器，该动力学与测量数据和假定噪声范围一致。最后，我们将开发的方法应用于数值示例。