Browse Prior Art Database

# Constraint Linear System Identification

IP.com Disclosure Number: IPCOM000082173D
Original Publication Date: 1974-Oct-01
Included in the Prior Art Database: 2005-Feb-28
Document File: 3 page(s) / 25K

IBM

## Related People

Todini, E: AUTHOR

## Abstract

This model allows the user to identify the impulse response w(r) for a lumped parameter linear system, when an input function i(t) and an output function q(t) are given together with the maximum estimated memory of the system t*.

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Constraint Linear System Identification

This model allows the user to identify the impulse response w(τ) for a lumped parameter linear system, when an input function i(t) and an output function q(t) are given together with the maximum estimated memory of the system t*.

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and its analytical formulation is:

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The proposed method is based on the minimization of the mean square error between computed and measured output functions:

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The model also allows the user to impose on the impulse response of the system one or more that one of the following physical constraints, which characterize the system:

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which can be written as follows, bearing in mind that i(t)=0 for t<0

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The program, by the user's choice, automatically sets up and solves one of the following problems:

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Since φ is a symmetric positive definite matrix, all the above mentioned problems have one and only one solution, which is obtained using a convex programming routine "SOLVER" due to Wilson, especially suited for quadratic programming.

For the determination of wj 0<=j<=m which minimizes the mean square error between computed and measured output functions from one of the four possible problems, besides the selection of the problem, the user must provide:

the input function ik 0<=k<=n

the output function qk 0<=k<=n

together with the maximum lag of the system (m) and the length of the output function (n).

The problem, a...