Gunther Reißig.
Convexity of reachable sets of nonlinear discrete-time systems.
Proc. 13th IEEE Int. Conf. Methods and Models in Automation and
Robotics (MMAR), Szczecin, Poland, Aug. 27 - 30, 2007,
pp. 199-204,
R. Kaszynski, ed., 2007.
Full text. (Free access.)
Abstract:
We present necessary and sufficient conditions for reachable
sets of discrete-time systems x(k+1) = F(k,x(k)) to be convex.
In particular, the set of states reachable at a given time
from a sufficiently small ellipsoid of initial states is always
convex if F is smooth enough,
and we provide explicit bounds on the size of those
ellipsoids.
Our results imply that outer discrete approximations
with approximation depth exceeding 1 can be readily computed up to
arbitrary precision.
A further potential application is outer polyhedral
approximation of reachable sets, which becomes
almost universally applicable if those sets are known to be
convex.
BibTeX entry:
@InProceedings{Reissig07aC,
author = {Gunther Rei{\ss}ig},
title = {Convexity of reachable sets of nonlinear discrete-time systems},
booktitle = {Proc. 13th IEEE Int. Conf. Methods and Models in Automation and Robotics (\nobreak{MMAR}), Szczecin, Poland, } # aug # { 27-30, 2007},
year = 2007,
pages = {199-204},
editor = {R. Kaszy{\'n}ski},
isbn = {978-83-751803-2-9 (abstracts), 978-83-751803-3-6 (CD)}
}
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