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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

Pierre Cardaliaguet
UFR Sciences Techniques, Lab. de Mathématiques, Université de Bretagne Occ., 6 Av. Victor Le Gorgeu, 29283 Brest, France


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.

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