Some Particular Classes of Performance Indices in Optimal Control

Abstract

There exist some particular classes of integral type performance indices in optimal control, which have been very little discussed. They, however, would be considerably important and helpful to design optimal control systems.
This paper deals with two classes of such performance indices. One is the “uncontrollable performance index” whose value becomes constant regardless of the control function. A sufficient condition of the functional form of its integrand for variour terminal conditions is discussed with some examples.
The other is the “degenerate performance index” whose value becomes minimal for some initial conditions when the control function is always zero during the control interval. A sufficient condition for this case and some examples are also presented.
Furthermore, an illustrative example shows that these two concepts are effective for analyzing the singular problems in optimal control by the use of quite different manner from ordinary methods.