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Some aspects of control tolerances and first-order sensitibity in optimal control systems

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1 Author(s)
Belanger, P. ; Foxboro Company, Digital Systems Divsion, Foxboro, MA, USA

This paper considers the effects of small control function variations of bounded magnitude. Two types of variations are considered: one, called "continual," is infinitesimally small over the control interval; the other, called "intermittent," is a pulse-type variation. If the control task is to take the system from an initial state to some target set, it is shown that, no matter how "tight" the control tolerances, there is always in general some control within tolerances which will cause the target to be missed. An exception to this rule is the case where the target is of dimensionality one less than that of the state-time space. Target sets not falling in this latter class are used in design as idealizations of actual target sets (e.g. a point is used instead of a small sphere). If a nominal control is found which takes the state to the ideal target, tolerances on this control are found such that the actual target will always be reached. If the nominal control is optimal with respect to the ideal set, giving some nominal cost, it is shown how one can find the possible cost variations resulting from the use of controls wthin the tolerance limits.

Published in:

Automatic Control, IEEE Transactions on  (Volume:11 ,  Issue: 1 )