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CHOOSING THE NOMINAL PATH FOR A DYNAMIC SYSTEM WITH RANDOM FORCING FUNCTIONS TO OPTIMIZE THE STATISTICAL PERFORMANCE,
HARVARD UNIV CAMBRIDGE MASS CRUFT LAB
When a dynamic system is subjected to random disturbances, the performance of the system must be judged in a probabilistic way. The ensemble-average performance is a useful criterion and leads, under the assumption of small amplitude disturbances, to mathematical problems which can be numerically solved with presently available techniques and computers. In this analysis the perturbations from a nominal path are assumed small enough that all terms above quadratic may be dropped when expanding about the nominal. If the mean values and correlations of the disturbances are given, the mean values and covariances of the perturbations may be calculated. The ensemble-average system performance depends on both the nominal path and the perturbation statistics. The purpose of this report is to analyze these dependences, in particular the coupling between them. Necessary conditions for the simultaneous optimization of the normal control variables plus gain matrices for linear estimation and feedback control systems are presented. The adaption of the steepest-ascent procedure for the simultaneous numerical optimization is discussed. Author
See also AD-604 006.