Journal of The Society of Instrument and Control Engineers

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This paper deals with the sensitivity synthesis of optimal control and the related problems.
Sensitivity functions and sensitivity equations are, at first, defined and derived for the four types of system parameter variations, that is, the ordinary parameter variation, the variation of initial conditions, the parameter variation which alters the order of the system and the variation of time delay parameter.
After it has been pointed out that the concept of the combined system which consists of a model system and its parameter sensitivity equation plays an important role in the sensitivity synthesis of optimal control, the controllability and the uncontrollability of the combined system are analyzed in detail, since the possibility of synthesizing the sensitivity optimal control depends on the controllability of the combined system.
The sensitivity synthesis of optimal control is introduced into the problem of terminal control in order to make the terminal constraints more rigid against the parameter variations. Comparing with the conventional synthesis, the effectiveness of the sensitivity synthesis is demonstrated by giving simple examples.
At last, the problem of synthesizing an optimal input for parameter identification is formulated from the view point of sensitivity. The concepts of unsynthesizability of an input and unidentifiability of a parameter are defined in terms of the signal invariance of an output from the combined system.

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