Perimeter estimates for reachable sets of control Systems

Journal of Convex Analysis

Volumn 13, Issue 2, 2006, Pages 253-267

  Cannarsa, Piermarco ^a   Cardaliaguet, Pierre ^b  

^a UNIVERSITY OF ROME TOR VERGATA   (Italy)

^b UNIVERSITÉ DE BRETAGNE OCCIDENTALE   (France)

Author keywords

Attainable sets; Control theory; Interior ball condition; Sets of finite perimeter

Indexed keywords

EID: 33747704858     PISSN: 09446532     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (12)

1. O. Alvarez, P. Cardaliaguet, R. Monneau: Existence and uniqueness for dislocation dynamics with positive velocity, Interfaces and Free Boundaries, to appear.
2. L. Ambrosio, N. Fusco, D. Pallara: Functions of Bounded Variation and Free Discontinuity Problems, Oxford Mathematical Monographs, Clarendon Press, Oxford (2000).
3. J. P. Aubin, H. Frankowska: Set-Valued Analysis, Birkhäuser, Boston (1990).
4. M. Bardi, I. Capuzzo-Dolcetta: Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations, Birkhäuser, Boston (1997).
5. P. Cannarsa, H. Frankowska: Interior sphere property of attainable sets and time optimal control, ESAIM: COCV, to appear.
6. P. Cannarsa, C. Sinestrari: Semiconcave Functions, Hamilton-Jacobi Equations and Optimal Control, Birkhäuser, Boston (2004).
7. P. Cannarsa, C. Pignotti, C. Sinestrari: Semiconcavity for optimal control problems with exit time, Discrete Contin. Dyn. Syst. 6(4) (2000) 975-997.
8. G. Colombo, A. Mariconda: Differentiability properties of a class of non-lipschitz functions, preprint (2004).
9. L. C. Evans, R. F. Gariepy: Measure Theory and Fine Properties of Functions, Studies in Advanced Mathematics, CRC Press, Boca Raton (1992).
10. H. Federer: Curvature measures, Trans. Amer. Math. Soc. 93 (1959) 418-491.
11. M. Quincampoix: Differential inclusions and target problems, SIAM J. Control Optim. 30(2) (1992) 324-335.
12. C. Sinestrari: Semiconcavity of the value function for exit time problems with nonsmooth target, Commun. Pure Appl. Anal. 3(4) (2004) 757-774.