計測と制御

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This discussion concerns the effects of noise and variation of system parameters on the iterative identification of a linear system by means of the learning identification method.
The progress of the learning method may be considered to occur in roughly two stages:
(1) the transient state (i. e. the initial stage of the approximation),
(2) the state of limit-accuracy (i. e. the state in which the precision as the ensemble average has become almost invariable).
In the former state, influence of initial error cannot still be ignored, and the length of the state represents, roughly speaking, the rate of identification. In the latter state, the approximations have nearly converged and are fluctuating in the neighbourhood of the true values of the unknown parameters according to the noise. The amplitude of the fluctuation determines the achievable accuracy of identification as the ensemble average.
In addition, there is an inconsistency between these two states: shortening of the transient state is incompatible with increase of accuracy. This incompatibility is examined quantitatively, and is made use of as a guiding principle in determining the error-correcting coefficient, α, of the learning method.
It is also shown that the method may be used to identify a slowly-varying non-stationary system which could not be identified by the stochastic approximation method, and influence of the variation of the non-stationary system parameters is investigated in some typical examples of non-stationary systems. In particular, the greatest attainable degree of limit-accuracy is obtained in several cases of non-stationary systems.
A discussion of optimal value of the error-correcting coefficient, α, is given in relation to the incompatibility, and an adaptive approximation method is proposed as a tentative means of resolving the incompatibility.

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