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中文摘要：
针对闭环条件下的子空间辨识问题，结合线性代数和几何学的基本概念，将输入输出误差序列包含至输入子空间中，基于输入扩张的状态空间构造方法，提出一种新的闭环辨识算法；解决开环算法应用于闭环系统辨识时产生有偏估计，甚至不能正确辨识的问题；实现闭环条件下对系统状态空间矩阵的强一致估计，并理论证明该辨识算法的强一致性；最后通过仿真实例验证本算法的有效性．
英文摘要：
For the basic problem of closed-loop identification, a new closed-loop identification algorithm is proposed in the framework of subspace method combined with linear algebra and geometry. In order to implement a new reconstruction of the state sequence, the output and input error sequences are included in the input subspace based on the augmented input. The estimation error, which is produced by open-loop algorithm when it is applied in the existence of feedback, is eliminated. The consistency estimate of system state-space matrices is implemented and the consistency property is proven in theory. Finally, the efficiency of this method is illustrated with a simulation example.
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