态空间系统的梯度优化辨识及收敛性分析

摘要

In order to solve the problem which was caused by the nonlinearity and nonconvexity between the output error and the system parameters in state-space model, proposed a gradient optimization identification for parameter estimation of state-space systems. Analyzed the principle of gradient identification based on local linearization. Moreover, determined the parameter search direction based on the QR and SVD methods. And gave the iterative identification algorithm for parameter estimation.Furthermore, analyzed the convergence of the identification algorithm and also gaven the analytic expression of the convergence rate of the identification algorithm. Finally, the effectiveness of the proposed method is illustrated by numerical simulation.%为解决状态空间系统的预报误差与系统参数之间的非线性、非凸性给参数估计带来的困难,提出了状态空间系统的梯度优化辨识方法.分析了基于局部线性化的梯度辨识原理,给出了基于QR分解、奇异值分解(SVD)确定参数搜索方向的实现方案,得到了估计系统参数的迭代辨识算法.探讨了算法的收敛性,给出了算法收敛速度的解析表达式,最后进行了数值仿真,实验结果说明了所提出方法的有效性.