Perimeter Estimates for Reachable Sets of Control Systems

The reachable set in time

,

{\cal R}(T) R ( T )

, is here investigated for the symmetric control system

\dot x (t)=f(x(t))u(t) x ˙ ( t ) = f ( x ( t ) ) u ( t )

,

u(t)\in\overline{B} u ( t ) ∈ B ‾

. It turns out that, for

f(x) f ( x )

smooth and nondegenerate,

{\cal R}(T) 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.