具有过程噪声和反馈操作的非线性连续时间系统的最佳线性逼近
Best Linear Approximation of Nonlinear Continuous-Time Systems Subject to Process Noise and Operating in Feedback
摘要：
在许多工程应用中，频率响应函数（FRF）测量中的非线性失真水平使用被称为随机相位多正弦和周期噪声的专门设计的周期激励信号来量化。该技术是基于最佳线性近似（BLA）的概念，它允许一个检查的线性框架的有效性与一个简单的实验。虽然经典的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，有必要将现有的BLA理论扩展到过程噪声的情况。在本文中，我们详细研究了过程噪声对非线性连续时间系统在闭环中运行的BLA的影响。结果表明，现有的非参数估计方法检测和量化的水平的非线性失真在频响测量仍然适用于过程噪声的存在。所有结果对离散时间系统和开环系统也是有效的。
英文摘要：
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.
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