The Selection of Performance Indices for Optimal Control Problems

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Abstract
This paper investigates the proper selection of a performance index to satisfy a word statement of desired effect. A performance index formed as the time integral of Un is solved for various values of n. When viewed in this light, the classical quadratic index (n = 2) gives a seemingly arbitrary solution. From this investigation the true optimal control solution can be ascertained. For the different values of n, solutions for totally different performance can be obtained. Performance indices combining two effects of minimum control effort and minimum response error are also investigated. The differences of a summed combination and a multiplicative combination are studied.

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