|
[1]
|
L. Adam and J. V. Outrata, On optimal control of a sweeping process coupled with an ordinary differential equation, Discrete Contin. Dyn. Syst.–Ser. B, 19 (2014), 2709-2738.
doi: 10.3934/dcdsb.2014.19.2709.
|
|
[2]
|
C. E. Arround and G. Colombo, A maximum principle of the controlled sweeping process, Set-Valued Var. Anal., 26 (2018), 607-629.
doi: 10.1007/s11228-017-0400-4.
|
|
[3]
|
M. Brokate and P. Krejčí, Optimal control of ODE systems involving a rate independent variational inequality, Discrete Contin. Dyn. Syst.–Ser. B, 18 (2013), 331-348.
doi: 10.3934/dcdsb.2013.18.331.
|
|
[4]
|
T. H. Cao and B. S. Mordukhovich, Optimal control of a perturbed sweeping process via discrete approximations, Discrete Contin. Dyn. Sysy.–Ser. B, 21 (2016), 3331-3358.
doi: 10.3934/dcdsb.2016100.
|
|
[5]
|
T. H. Cao and B. S. Mordukhovich, Optimality conditions for a controlled sweeping process with applications to the crowd motion model, Discrete Contin. Dyn. Syst.-Ser. B, 22 (2017), 267-306.
doi: 10.3934/dcdsb.2017014.
|
|
[6]
|
T. H. Cao and B. S. Mordukhovich, Optimal control of a nonconvex perturbed sweeping process, J. Diff. Eqs., 266 (2019), 1003-1050.
doi: 10.1016/j.jde.2018.07.066.
|
|
[7]
|
F. H. Clarke, Yu. S Ledyaev, R. J. Stern and P. R. Wolenski, Nonsmooth Analysis and Control Theory, Springer, 1998.
|
|
[8]
|
G. Colombo, R. Henrion, N. D. Hoang and B. S. Mordukhovich, Optimal control of the sweeping process, Dyn. Contin. Discrete Impuls. Syst.–Ser. B, 19 (2012), 117-159.
|
|
[9]
|
G. Colombo, R. Henrion, N. D. Hoang and B. S. Mordukhovich, Optimal control of the sweeping process over polyhedral controlled sets, J. Diff. Eqs., 260 (2016), 3397-3447.
doi: 10.1016/j.jde.2015.10.039.
|
|
[10]
|
G. Colombo and L. Thibault, Prox-regular sets and applications, Handbook of Nonconvex Analysis, International Press, (2010), 99–182.
|
|
[11]
|
M. d. R. de Pinho, M. M. A. Ferreira and G. V. Smirnov, Optimal control involving sweeping processes, Set-Valued Var. Anal., 2018, 1–26.
doi: 10.1007/s11228-018-0501-8.
|
|
[12]
|
T. Donchev, E. Farkhi and B. S. Mordukhovich, Discrete approximations, relaxation, and optimization of one-sided Lipschitzian differential inclusions in Hilbert spaces, J. Diff. Eqs., 243 (2007), 301-328.
doi: 10.1016/j.jde.2007.05.011.
|
|
[13]
|
J. F. Edmond and L. Thibault, Relaxation of an optimal control problem involving a perturbed sweeping process, Math. Program., 104 (2005), 347-373.
doi: 10.1007/s10107-005-0619-y.
|
|
[14]
|
P. E. Kloeden and E. Platen., Numerical Solution of Stochastic Differential Equations., Springer, 1992.
doi: 10.1007/978-3-662-12616-5.
|
|
[15]
|
B. Maury and J. Venel, A discrete model for crowd motion, ESAIM: M2AN, 45 (2011), 145-168.
doi: 10.1051/m2an/2010035.
|
|
[16]
|
B. S. Mordukhovich, Discrete approximations and refined Euler-Lagrange conditions for differential inclusions, SIAM J. Control Optim., 33 (1995), 882-915.
doi: 10.1137/S0363012993245665.
|
|
[17]
|
B. S. Mordukhovich, Variational Analysis and Generalized Differentiation, Ⅰ: Basic Theory, Springer, 2006.
|
|
[18]
|
B. S. Mordukhovich, Variational Analysis and Generalized Differentiation, Ⅱ: Applications, Springer, 2006.
|
|
[19]
|
J. J. Moreau, On unilateral constraints, friction and plasticity, New Variational Techniques in Mathematical Physics, Proceedings of C.I.M.E. Summer Schools, pages 173–322. Cremonese, 1974.
|
|
[20]
|
R. T. Rockafellar and R. J.-B. Wets, Variational Analysis, Springer-Verlag, Berlin, 1998.
doi: 10.1007/978-3-642-02431-3.
|
|
[21]
|
A. A. Tolstonogov, Control sweeping process, J. Convex Anal., 23 (2016), 1099-1123.
|
|
[22]
|
J. Venel, A numerical scheme for a class of sweeping process, Numerische Mathematik, 118 (2011), 367-400.
doi: 10.1007/s00211-010-0329-0.
|
|
[23]
|
R. B. Vinter, Optimal Control, Birkhaüser, 2000.
|
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