# Geometric Approaches to Control in the Presence of Magnitude and Rate Saturations

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Richard M. Murray

In *The Astrom Symposium on Control*, pp. 43-72

This paper gives a survey of some recent results on control of systems with magnitude
and rate limits, motivated by problems in real-time trajectory generation and tracking for
unmanned aerial vehicles. Two problems are considered: stabilization using ``nonlinear
wrappers* to rescale a given control law and real-time trajectory generation using*
differential flatness. For both problems, simplified versions of the general problem are
studied using tools from differential geometry and nonlinear control to give insights into
the limitations imposed by magnitude and rate limits and provide insights into
constructive solutions to the trajectory generation and tracking problems.

- CDS Technical

Report: http://www.cds.caltech.edu/~murray/preprints/mur99-lund.pdf

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