Convergence of Hierarchical Stochastic Gradient Identification for Transfer Function Matrix Model
传递函数阵递阶随机梯度辨识方法的收敛性分析(英文)

The hierarchical identification principle is stated, and the hierarchical stochastic gradient (HSG) algorithm for the transfer function matrix (TFM) model for multivariable systems is presented. In the hierarchical identification, the system parameters are divided into the parameter vector, which includes the coefficients of the characteristic polynomial of the system, and the parameter matrix, which includes the coefficients of the numerators of the TFM polynomials, respectively. The convergence analysis, using martingale hyperconvergence theorem, shows that the parameter estimation error (PEE) given by the HSG algorithm is consistently bounded, and that PEE consistently converges to zero under the persistent excitation condition. Hierarchical identification has a small amount of calculation and is easy to be realized.