论文标题
非线性系统的数据驱动控制：超越多项式动力学
Data-Driven Control of Nonlinear Systems: Beyond Polynomial Dynamics
论文作者
论文摘要
在本文中，我们为连续时间非线性系统提出了一种数据驱动的控制器设计方法，没有使用模型知识，而仅测量受噪声影响的数据。尽管大多数现有的方法都集中在具有多项式动力学的系统上，但我们的方法允许为具有合理或一般非物质动力学的未知系统设计控制器。我们首先得出具有有理动力学的未知非线性系统的数据驱动参数化。通过将强大的控制技术应用于此参数化，我们获得了基于平方的标准，用于设计具有与测量数据和假定噪声结合的所有系统的闭环稳定性和性能保证。然后，我们将这种方法应用于控制系统，其动力学在一般非多项式基础函数中是线性通过将其转换为多项式系统的线性。最后，我们将开发的方法应用于数值示例。
In this paper, we present a data-driven controller design method for continuous-time nonlinear systems, using no model knowledge but only measured data affected by noise. While most existing approaches focus on systems with polynomial dynamics, our approach allows to design controllers for unknown systems with rational or general non-polynomial dynamics. We first derive a data-driven parametrization 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 and performance guarantees for all systems which are consistent with the measured data and the assumed noise bound. We then apply this approach to control systems whose dynamics are linear in general non-polynomial basis functions by transforming them into polynomial systems. Finally, we apply the developed approaches to numerical examples.
