an:05046589
Zbl 1114.93018
Cannarsa, Piermarco; Cardaliaguet, Pierre
Perimeter estimates for reachable sets of control systems
EN
J. Convex Anal. 13, No. 2, 253-267 (2006).
00185180
2006
j
93B03 93C15 49J15 93C10 93B05
nonlinear control systems; reachable sets; continuous-time systems
In the paper nonlinear, finite-dimensional, continuous-time control systems with constant coefficient are considered. The main purpose is to investigate regularity of the reachable set for constrained controls. Using theory of nonlinear ordinary differential equations and functional analysis under some additional assumptions on nonlinear function in the state equation, several properties of the reachable sets are formulated and proved. Moreover, many remarks and comments on reachable sets are also presented. Finally, it should be pointed out, that similar problems have been recently considered in the paper of \textit{C. Sinestrari} [Commun. Pure Appl. Anal. 13, No. 4, 757--774 (2004; Zbl 1064.49024)] and in the monograph of \textit{J. P. Aubin} and \textit{H. Frankowska} [Set-valued analysis', Boston etc.: Birkh??user (1990; Zbl 0713.49021)].
Jerzy Klamka (Gliwice)
Zbl 1064.49024; Zbl 0713.49021