随机状态空间系统的梯度优化辨识

System identification of stochastic state-space systems by gradient optimization search

提出了随机状态空间系统参数的梯度优化辨识方法。通过极小化输出预报误差而获得系统的参数估计。提出了动态选择雅可比矩阵奇异值比率确定参数搜索方向的方法,用以解决因雅可比矩阵的线性相关性引起的算法失效问题。给出了融合参数局部逼近性能信息的辨识算法,并得到了算法收敛速度的解析表达式。数值仿真实验的结果说明了所提出方法的有效性。

System identification based on gradient optimization search is proposed for parameter estimation of stochastic state-space systems.The system parameters are estimated by optimizing an output-error cost function.Moreover,the search direction is determined by dynamic singular ration of Jacobian matrix for the purpose of solving the algorithm failure caused by the rank-deficient Jacobians.In addition, identification algorithm by considering the local linear approximation of the output error is presented.Furthermore,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.