论文标题
具有嘈杂数据的非线性多项式系统的数据驱动稳定
Data-driven stabilization of nonlinear polynomial systems with noisy data
论文作者
论文摘要
在最近的一篇论文中，我们通过求解线性矩阵不等式，展示了如何使用有限尺寸的嘈杂数据来学习未知线性系统的控制器。在本说明中，我们通过以数据依赖的正方形程序总和的形式制定稳定证书来扩展这种方法来处理未知的非线性多项式系统，该计划的解决方案直接提供了稳定的控制器和Lyapunov函数。然后，我们得出该结果的变化，从而导致更有利的控制器设计。结果还揭示了与设计控制器从多项式系统的最小二乘估计开始的问题的联系。
In a recent paper we have shown how to learn controllers for unknown linear systems using finite-sized noisy data by solving linear matrix inequalities. In this note we extend this approach to deal with unknown nonlinear polynomial systems by formulating stability certificates in the form of data-dependent sum of squares programs, whose solution directly provides a stabilizing controller and a Lyapunov function. We then derive variations of this result that lead to more advantageous controller designs. The results also reveal connections to the problem of designing a controller starting from a least-square estimate of the polynomial system.
