一种新的基于遗忘因子的递推子空间辨识算法

针对工业系统中广泛存在的时变特性, 提出一种新的递推子空间辨识算法, 实现对系统状态空间模型的在线递推估计. 为更好地跟踪系统时变特性, 研究基于遗忘因子的输入输出数据矩阵构造机制, 以提高递推算法的收敛速度; 针对算法中奇异值分解的求解问题, 将梯度型算法引入基于遗忘因子的状态子空间跟踪中, 实现对广义能观测矩阵的估计, 避免了子空间近似带来的估计有偏性; 该算法计算简单有效, 且对初值具有更高的鲁棒性; 最后给出该递推算法的性能分析, 理论证明其收敛性, 并通过仿真实例验证算法的有效性.

A novel recursive MOESP subspace identification algorithm based on forgetting factor

A new recursive subspace identification algorithm is proposed for the recursive estimation of state space model of linear time-varying systems. A forgetting factor is introduced in the Hankel matrices of the input-output data to increase the convergent rate and improve the performance in tracking the time-varying information. In solving the singular value decomposition (SVD) problem, a gradient-type subspace tracking method is employed to update the state-space subspace based on forgetting factor, realizing the unbiased estimation of the extended observability matrix and improving the robustness to the uncertainty in initial values. The proposed method is simple and highly accurate in numerical computation. The convergence of the proposed method is also proved theoretically. Finally, the efficiency of this method is illustrated with a simulation example.