Abstract

The reachable set in time T>0T>0, R(T){\cal R}(T), is here investigated for the symmetric control system x˙(t)=f(x(t))u(t)\dot x (t)=f(x(t))u(t), u(t)∈B‾u(t)\in\overline{B}. It turns out that, for f(x)f(x) smooth and nondegenerate, R(T){\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.

Author information

Contact details are reproduced from the original publication and may be historical.

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, 29285 Brest, France

Pierre.Cardaliaguet@univ-brest.fr

Keywords

  • Control theory
  • attainable sets
  • interior ball condition
  • sets of finite perimeter

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Suggested citation

P. Cannarsa, P. Cardaliaguet. “Perimeter Estimates for Reachable Sets of Control Systems.” Journal of Convex Analysis 13 (2006), No. 2, 253–267. https://doi.org/10.68381/jca13024

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Published by Heldermann Verlag, 2006. Rights now held by Banach Press.