论文标题
非线性连续时系统的最佳线性近似可能会受到过程噪声的影响，并在反馈中运行
Best Linear Approximation of Nonlinear Continuous-Time Systems Subject to Process Noise and Operating in Feedback
论文作者
论文摘要
在许多工程应用中，使用特殊设计的周期性激发信号（称为随机相多差和周期性噪声）来量化频率响应函数（FRF）测量的非线性畸变水平。该技术基于最佳线性近似（BLA）的概念，并且可以通过简单的实验检查线性框架的有效性。尽管经典的BLA理论只能处理测量噪声，但在大多数应用中，系统产生的噪声（称为过程噪声）是主要的噪声源。因此，需要将现有的BLA理论扩展到过程噪声案例。在本文中，我们详细研究了过程噪声对在闭环中运行的非线性连续时间系统BLA的影响。结果表明，用于检测和量化FRF测量中非线性畸变水平的现有非参数估计方法仍然适用于过程噪声的存在。所有结果也适用于开放循环运行的离散时间系统和系统。
In many engineering applications the level of nonlinear distortions in frequency response function (FRF) measurements is quantified using specially designed periodic excitation signals called random phase multisines and periodic noise. The technique is based on the concept of the best linear approximation (BLA) and it allows one to check the validity of the linear framework with a simple experiment. Although the classical BLA theory can handle measurement noise only, in most applications the noise generated by the system -- called process noise -- is the dominant noise source. Therefore, there is a need to extend the existing BLA theory to the process noise case. In this paper we study in detail the impact of the process noise on the BLA of nonlinear continuous-time systems operating in a closed loop. It is shown that the existing nonparametric estimation methods for detecting and quantifying the level of nonlinear distortions in FRF measurements are still applicable in the presence of process noise. All results are also valid for discrete-time systems and systems operating in open loop.
