Stochastic inverse problems on identification of feedback system

在由平稳高斯过程描述的反馈系统中，开环传递函数在一定条件下可以辨识，其中与反馈系统等价的新息模型所对应的Riccati方程有稳定的特解。为了实现对它们的识别，还需要进行模型降阶。在可辨识条件下的反馈系统由自回归模型辨识的情况下，由于原始反馈模型和自回归模型之间的结构间隙，存在偏差问题。指出开环传递函数的辨识存在自回归模型阶数依赖的偏差，从实际应用出发，有必要将输入输出个数相同的反馈系统的辨识问题推广到输入输出个数不同的反馈系统的辨识问题。为了处理非方矩阵，在广义Riccati方程中引入广义逆矩阵，从而在广义最小相位条件下，非方反馈系统的新息模型是伪方的。研究了三反馈系统的伪平方新息模型，以理解开环传递函数辨识的不一致性。在三反馈系统中存在三种类型的辨识问题。从随机反问题的观点出发，从观测变量的组合出发，研究了标量型、向量型和收缩型新息模型。

In a feedback system described by a stationary Gaussian process open loop transfer functions can be identified under some conditions, where an associate Riccati equation related to an innovation model equivalent to the feedback system has a stable particular solution. The model reduction is also needed for achievement of identification of them. Where the feedback system under the identifiable condition is identified by an autoregressive model, there remains a bias problem due to structure gaps between the original feedback model and the autoregressive model. It is reported that identified open loop transfer functions have a bias of order-dependence of the autoregressive model.From practical applications it is necessary to extend the identification problem of feedback system with the same number of inputs and outputs to that with different number of inputs and outputs. To treat non-square matrices the generalized inverse matrix is used in the generalized Riccati equation, and then the innovation model of non-square feedback system is pseudo-square under a generalized minimum phase condition. The pseudo-square innovation model is studied in a tri-feedback system to understand inconsistency of identification of open loop transfer functions. There are three types of identification problems in the tri-feedback system. From combination of observation variables a scalar type, a vector type and a contracted type of innovation model are studied from the viewpoint of stochastic inverse problem.