In this work, we study the existence of solutions of a perturbed sweeping process and of a time optimal control problem under a condition on the perturbation that is strictly weaker than the usual assumption of convexity.
DOI : 10.1051/cocv/2015036
Mots-clés : Differential inclusion, almost convex set, attainable set
@article{COCV_2017__23_1_1_0,
author = {Affane, Doria and Azzam-Laouir, Dalila},
title = {Almost convex valued perturbation to time optimal control sweeping processes},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {1--12},
publisher = {EDP-Sciences},
volume = {23},
number = {1},
year = {2017},
doi = {10.1051/cocv/2015036},
mrnumber = {3601013},
zbl = {1366.34029},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/cocv/2015036/}
}
TY - JOUR AU - Affane, Doria AU - Azzam-Laouir, Dalila TI - Almost convex valued perturbation to time optimal control sweeping processes JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2017 SP - 1 EP - 12 VL - 23 IS - 1 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2015036/ DO - 10.1051/cocv/2015036 LA - en ID - COCV_2017__23_1_1_0 ER -
%0 Journal Article %A Affane, Doria %A Azzam-Laouir, Dalila %T Almost convex valued perturbation to time optimal control sweeping processes %J ESAIM: Control, Optimisation and Calculus of Variations %D 2017 %P 1-12 %V 23 %N 1 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2015036/ %R 10.1051/cocv/2015036 %G en %F COCV_2017__23_1_1_0
Affane, Doria; Azzam-Laouir, Dalila. Almost convex valued perturbation to time optimal control sweeping processes. ESAIM: Control, Optimisation and Calculus of Variations, Tome 23 (2017) no. 1, pp. 1-12. doi : 10.1051/cocv/2015036. http://archive.numdam.org/articles/10.1051/cocv/2015036/
and , Second-order differential inclusions with almost convex right-hand sides. Electron. J. Qual. Theory Differ. Equ. 34 (2011) 1–14. | MR | Zbl
J.P. Aubin and A. Cellina, Differential inclusions set valued maps and viability theory. Springer-Verlag, Berlin (1984). | MR | Zbl
and , Nonconvex sweeping process and prox-regularity in Hilbert space. J. Nonlinear Convex Anal. 6 (2005) 359–374. | MR | Zbl
C. Castaing and M. Valadier, Convex analysis and measurable multifunctions. Vol. 580 of Lect. Notes Math. Springer-Verlag, Berlin (1977). | MR | Zbl
and , Evolution problems associated with nonconvex closed moving sets. Portugal. Math. 53 (1996) 73–87. | MR | Zbl
, and , Evolution equations governed by the sweeping process. Set-Valued Anal. 1 (1993) 109–139. | DOI | MR | Zbl
, and , Functional evolution equations governed by nonconvex sweeping process. J. Nonlin. Convex Anal. 2 (2001) 217–241. | MR | Zbl
and , On a classical problem of the calculus of variations without convexity assumption. Ann. Inst. Henri Poincaré, Anal. Non Linéaire 7 (1990) 97–106. | DOI | Numdam | MR | Zbl
and , Existence of solution to differential inclusion and optimal control problems in the autonomous case. Siam J. Control Optim. 42 (2003) 260–265. | DOI | MR | Zbl
F.H. Clarke, Optimization and Nonsmooth Analysis. John Wiley and Sons (1983). | MR | Zbl
, and , Proximal smoothness and the lower property. J. Convex Anal. 2 (1995) 117–144. | MR | Zbl
, On certain questions in the theory of optimal control. Vestnik. Univ., Ser. Mat. Mech. 2 (1959) 25–32; Translated in [SIAM J. Control 1 (1962) 76–84]. | MR | Zbl
, and , Local differentiability of distance functions. Trans. Math. Soc. 352 (2000) 5231–5249. | DOI | MR | Zbl
Cité par Sources :
