1998 Fiscal Year Final Research Report Summary
Stochastic inverse problems on identification of feedback system
| Project/Area Number |
08680329
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Statistical science
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| Research Institution | Gifu University |
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Principal Investigator |
KISHIDA Kuniharu Gifu University, Facylty of Engineering, Department of Information Science, Professor, 工学部, 教授 (90115402)
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| Project Period (FY) |
1996 – 1998
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| Keywords | inverse problem / system identification / fluctuation analysis / feedback system / innovation model / transfer functions / contraction of information |
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| Research Abstract |
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.
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