Journal of Convex Analysis 13 (2006), No. 2, 253--267
Copyright Heldermann Verlag 2006
Perimeter Estimates for Reachable Sets of Control Systems
Piermarco Cannarsa
Dip. di Matematica, Università di Roma Tor Vergata, Via della Ricerca Scientifica 1, 00133 Roma, Italy
cannarsa@axp.mat.uniroma2.it
Pierre Cardaliaguet
UFR Sciences Techniques, Lab. de Mathématiques, Université de Bretagne Occ., 6 Av. Victor Le Gorgeu, 29283 Brest, France
Pierre.Cardaliaguet@univ-brest.fr
[Abstract-pdf]
The reachable set in time $T>0$, ${\cal R}(T)$, is here investigated for the symmetric control system $\dot x (t)=f(x(t))u(t)$, $u(t)\in\overline{B}$. It turns out that, for $f(x)$ smooth and nondegenerate, ${\cal R}(T)$ has finite perimeter, and a sharp estimate for the time-dependence of the perimeter and volume of such a set can be obtained.
Keywords: Control theory, attainable sets, interior ball condition, sets of finite perimeter.
[ Fulltext-pdf (436 KB)] for subscribers only.