非线性随机系统具有遗忘因子的递推最小二乘法

Recursive least squares of nonlinear stochastic system owns forgetting factor

针对NARMAX模型,结合线性滤波、谱分解定理及成型滤波器原理构成非线性随机系统模型,并将参数模型转化为脉冲响应非参数模型。依据Hankel矩阵法,在参数估计准则函数中加入待估参数的增量约束项和遗忘因子,并结合增广最小二乘递推算法,提出一种具有遗忘因子的非线性参数估计的递推最小二乘法。该算法收敛速度快,且能克服病态,适用于时变参数情形。将其应用于一种非线性自适应预测控制算法仿真中,验证了算法的有效性。

Aimed at NARMAX model, this paper, in combination with linear filter, spectral decomposition theorems and the principle of shaping liher, introduces the development of the nonlinear random system model and the conversion of parameter model into impulse response nonparametric model. Based on Hankel＇ s matrix method and augmented least square recursive algorithm, the paper features the recursive least squares method of nonlinear parameter estimation with forgetting factor by introducing the constraint indicator of incremental and forgetting factor of pending parameter into criterion function of param- eter estimation. Capable of giving higher convergence speed and getting over ill-condition, the suggested algorithm lends itself to the time-varying parameter condition. The validity is proved by its use in simulation of nonlinear adaptive predictive control algorithms.