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.
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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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