态空间系统的梯度优化辨识及收敛性分析*

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。

Gradient optimization identification for state-space systems and convergence analysis

In order to solve the problem which is caused by the nonlinearity and nonconvexity between the output error and the system parameters in state-space model, gradient optimization identification is proposed for parameter estimation of state-space systems. The principle of gradient identification based-on local linearization is analyzed. Moreover, the parameter search direction is determined based on the QR and SVD methods. And iterative identification algorithm is given for parameter estimation. Furthermore, the convergence of the identification algorithm is analyzed and the analytic expression of the convergence rate of the identification algorithm is also given. Finally, the effectiveness of the proposed method is illustrated by numerical simulation.