4,703 research outputs found
On K\"ahler metrisability of two-dimensional complex projective structures
We derive necessary conditions for a complex projective structure on a
complex surface to arise via the Levi-Civita connection of a (pseudo-)K\"ahler
metric. Furthermore we show that the (pseudo-)K\"ahler metrics defined on some
domain in the projective plane which are compatible with the standard complex
projective structure are in one-to-one correspondence with the hermitian forms
on whose rank is at least two. This is achieved by prolonging
the relevant finite-type first order linear differential system to closed form.
Along the way we derive the complex projective Weyl and Liouville curvature
using the language of Cartan geometries.Comment: 17 pages, exposition improved, typos corrected, references adde
System identification for modeling for control of flexible structures
The major components of a design and operational flight strategy for flexible structure control systems are presented. In this strategy an initial distributed parameter control design is developed and implemented from available ground test data and on-orbit identification using sophisticated modeling and synthesis techniques. The reliability of this high performance controller is directly linked to the accuracy of the parameters on which the design is based. Because uncertainties inevitably grow without system monitoring, maintaining the control system requires an active on-line system identification function to supply parameter updates and covariance information. Control laws can then be modified to improve performance when the error envelopes are decreased. In terms of system safety and stability the covariance information is of equal importance as the parameter values themselves. If the on-line system ID function detects an increase in parameter error covariances, then corresponding adjustments must be made in the control laws to increase robustness. If the error covariances exceed some threshold, an autonomous calibration sequence could be initiated to restore the error enveloped to an acceptable level
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