反馈非线性系统随机梯度辨识算法及其收敛性

反馈非线性受控自回归系统是由前向通道的受控自回归模型和反馈通道的静态非线性构成, 这类系统经过参数化后得到双线性参数辨识模型. 本文通过对辨识模型中双线性参数乘积项进行分解, 基于梯度搜索原理, 提 出了反馈非线性系统的随机梯度辨识算法. 为了改善随机梯度算法的收敛速度, 引入遗忘因子, 文章给出了遗忘因子随机梯度算法, 利用随机过程理论, 建立了随机梯度算法的参数估计收敛定理, 证明了算法的收敛性. 最后, 通过数值仿真验证了算法的有效性.

Stochastic gradient identification algorithm and its convergence for feedback nonlinear systems

Through the parameterization, we obtain the bilinear-parameter identification model of the feedback nonlinear controlled autoregressive system, which is composed of a controlled autoregressive model in the forward channel and a static nonlinearity in the feedback channel. By decomposing the product term of the bilinear parameters in the identification model, a stochastic gradient identification algorithm is developed to estimate the unknown parameters of the feedback nonlinear system based on the gradient search. In order to improve the convergence rate of the proposed stochastic gradient algorithm, the forgetting factor stochastic gradient algorithm is given by introducing the forgetting factor. Also, this paper establishes the convergence theorem of the parameter estimation and proves the convergence of the proposed stochastic gradient algorithm by means of the stochastic process theory. Finally, the simulation example is carried out to verify the effectiveness of the proposed algorithms from the aspects of parameter estimation accuracy and prediction performance.