This paper studies the attainable set at time for the control system
Mots-clés : control theory, attainable sets, minimum time function, semiconcave functions
@article{COCV_2006__12_2_350_0, author = {Cannarsa, Piermarco and Frankowska, H\'el\`ene}, title = {Interior sphere property of attainable sets and time optimal control problems}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {350--370}, publisher = {EDP-Sciences}, volume = {12}, number = {2}, year = {2006}, doi = {10.1051/cocv:2006002}, mrnumber = {2209357}, zbl = {1105.93007}, language = {en}, url = {http://www.numdam.org/articles/10.1051/cocv:2006002/} }
TY - JOUR AU - Cannarsa, Piermarco AU - Frankowska, Hélène TI - Interior sphere property of attainable sets and time optimal control problems JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2006 SP - 350 EP - 370 VL - 12 IS - 2 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv:2006002/ DO - 10.1051/cocv:2006002 LA - en ID - COCV_2006__12_2_350_0 ER -
%0 Journal Article %A Cannarsa, Piermarco %A Frankowska, Hélène %T Interior sphere property of attainable sets and time optimal control problems %J ESAIM: Control, Optimisation and Calculus of Variations %D 2006 %P 350-370 %V 12 %N 2 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv:2006002/ %R 10.1051/cocv:2006002 %G en %F COCV_2006__12_2_350_0
Cannarsa, Piermarco; Frankowska, Hélène. Interior sphere property of attainable sets and time optimal control problems. ESAIM: Control, Optimisation and Calculus of Variations, Tome 12 (2006) no. 2, pp. 350-370. doi : 10.1051/cocv:2006002. http://www.numdam.org/articles/10.1051/cocv:2006002/
[1] Differential Inclusions. Springer-Verlag, Berlin (1984). | MR | Zbl
, ,[2] Set-Valued Analysis. Birkhäuser, Boston (1990). | MR | Zbl
, ,[3] Optimal control and viscosity solutions of Hamilton-Jacobi equations. Birkhäuser, Boston (1997). | Zbl
, ,[4] An approximation scheme for the minimum time function. SIAM J. Control Optim. 28 (1990) 950-965. | Zbl
, ,[5] On two conjectures by Hájek. Funkcial. Ekvac. 23 (1980) 221-227. | Zbl
,[6] Perimeter estimates for the reachable set of control problems. J. Convex. Anal. (to appear). | MR | Zbl
, ,[7] Semiconcavity for optimal control problems with exit time. Discrete Contin. Dynam. Syst. 6 (2000) 975-997. | Zbl
, , ,[8] Convexity properties of the minimum time function. Calc. Var. 3 (1995) 273-298. | Zbl
, ,[9] Semiconcave functions, Hamilton-Jacobi equations and optimal control. Birkhäuser, Boston (2004). | MR | Zbl
, ,[10] Optimization and nonsmooth analysis. Wiley, New York (1983). | MR | Zbl
,[11] Processi di controllo lineari in . Quad. Unione Mat. Italiana 30, Pitagora, Bologna (1985). | Zbl
,[12] Shape analysis via oriented distance functions. J. Funct. Anal. 123 (1994) 129-201. | Zbl
, ,[13] Linearization and boundary trajectories of nonsmooth control systems. Canad. J. Math. 40 (1988) 589-609. | Zbl
, ,[14] Functional analysis and time optimal control. Academic Press, New York (1969). | MR | Zbl
, ,[15] Foundations of optimal control theory. John Wiley & Sons Inc., New York (1967). | MR | Zbl
, ,[16] Necessary conditions for a nonlinear control system. J. Differ. Equ., 59, 257-265. | Zbl
, , ,[17] On the Bellman function for the time-optimal process problem. J. Appl. Math. Mech. 34 (1970) 785-791. | Zbl
,[18] Accessible sets in control theory. Int. Conf. on Diff. Eqs., Academic Press (1975) 646-650. | Zbl
,[19] Variational analysis. Springer-Verlag, Berlin (1998). | MR | Zbl
, ,[20] Semiconcavity of the value function for exit time problems with nonsmooth target. Communications on Pure and Applied Analysis. Commun. Pure Appl. Anal. 3 (2004) 757-774. | Zbl
,[21] Lipschitz continuity of the value function in optimal control. J. Optim. Theory Appl. 94 (1997) 335-363. | Zbl
,[22] Proximal analysis and the minimal time function. SIAM J. Control Optim. 36 (1998) 1048-1072. | Zbl
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