基于KRLS的非均匀采样非线性系统辨识

利用提升技术可将非均匀采样非线性系统离散化为一个多输入单输出传递函数模型,从而将系统输出表示为非均匀刷新非线性输入和输出回归项的线性参数模型,进一步基于非线性输入的估计或过参数化方法进行辨识.然而,当非线性环节结构未知或不能被可测非均匀输入参数化表示时,上述辨识方法将不再适用.为了解决这个问题,利用核方法将原始非线性数据投影到高维特征空间中使其线性可分,再对投影后的数据应用递推最小二乘算法进行辨识,提出基于核递推最小二乘的非均匀采样非线性系统辨识方法.此外,针对系统含有有色噪声干扰的情况,参考递推增广最小二乘算法的思想,利用估计残差代替不可测噪声,提出核递推增广最小二乘算法.最后,通过仿真例子验证所提算法的有效性.

Identification of non-uniformly sampled nonlinear systems based on KRLS

Using the lifting technique to discretize the non-uniformly sampled nonlinear system into a multiple input single output transfer function model, the system output can be represented as a linear parameter model with non-uniform updating nonlinear input and ouput regressors, and the system can be further identified based on the estimates of nonlinear inputs or the overparameterization method. However, when the nonlinear structure is unknown or cannot be parameterized by the measurable non-uniform inputs, the above mentioned identification methods will no longer apply. In order to solve this problem, the kernel method is applied to project original nonlinear data into a high dimensional feature space to make it linearly separable, and then the recursive least squares algorithm is used to identify the projected data, thus a kernel recursive least squares identification algorithm is proposed for non-uniformly sampled nonlinear systems. In addition, refering to the idea of recursive extened least squares algorithm, replacing the unmeasured noise with the estimated residual error, the kernel recursive extended least squares algorithm is proposed for systems with colored noise interference. Finally, numerical simulation examples verify the effectiveness of the proposed algorithms.