Optimal control of the sweeping process

Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms

Volumn 19, Issue 1-2, 2012, Pages 117-159

  Colombo, G ^a   Henrion, R ^b   Hoang, N D ^c   Mordukhovich, B S ^c  

^a UNIVERSITY OF PADOVA   (Italy)

^b WEIERSTRASS INSTITUTE FOR APPLIED ANALYSIS AND STOCHASTICS   (Germany)

^c WAYNE STATE UNIVERSITY   (United States)

Author keywords

Dissipative differential inclusions; Generalized differentiation; Optimal control; Sweeping process; Variational analysis

Indexed keywords

EID: 84857332981     PISSN: 14928760     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (19)

1. Attouch, H., Buttazzo, Michaille, G.: Variational Analysis in Sobolev and BV Spaces: Applications to PDEs and Optimization, SIAM, Philadelphia, 2005
2. Borwein, J. M., Zhu, Q. J.: Techniques of Variational Analysis, Springer, New York, 2005
3. Clarke, F. H.: Necessary conditions in dynamic optimization, Mem. Amer. Math. Soc. 173, No. 816, 2006
4. Colombo, G., Thibault, L.: Prox-regular sets and applications, in Handbook of Nonconvex Analysis (D. Y. Gao, D. Motreanu, eds.), International Press, Boston, 2010
5. Donchev, T., Farkhi, E., Mordukhovich, B. S.: Discrete approximations, relaxation, and optimization of one-sided Lipschitzian differential inclusions in Hilbert spaces, J. Diff. Eq. 243 (2007), 301-328
6. Henrion, R., Mordukhovich, B. S., Nam, N. M.: Second-order analysis of polyhedral systems in finite and infinite dimensions with applications to robust stability of variational inequalities, SIAM J. Optim. 20 (2010), 2199-2227
7. Ioffe, A. D.: Euler-Lagrange and Hamiltonian formalisms in dynamic optimization, Trans. Amer. Math. Soc. 349 (1997), 2871-2900
8. Krejčí, P., Vladimirov, A.: Polyhedral sweeping processes with oblique reflection in the space of regulated functions, Set-Valued Anal. 11 (2003), 91-110
9. Loewen, P. D., Rockafellar, R. T.: New necessary conditions for the generalized problem of Bolza, SIAM J. Control Optim. 345 (1996), 1496-1511 (Pubitemid 126572922)
10. Monteiro Marques, M. D. P.: Differential Inclusions in Nonsmooth Mechanical Problems: Shocks and Dry Friction, Birkhäuser, Boston, 1993
11. Mordukhovich, B. S.: Discrete approximations and refined Euler-Lagrange conditions for differential inclusions, SIAM J. Control Optim. 33 (1995), 882-915
12. Mordukhovich, B. S.: Variational Analysis and Generalized Differentiation, I: Basic Theory, Springer, Berlin, 2006
13. Mordukhovich, B. S.: Variational Analysis and Generalized Differentiation, II: Applications, Springer, Berlin, 2006
14. Moreau, J.-J.: On unilateral constraints, friction and plasticity, in New Variational Techniques in Mathematical Physics, Proceedings from CIME (G. Capriz, G. Stampacchia, eds.), Cremonese, Rome (1974), 173-322
15. Moreau, J.-J.: Evolution problem associated with a moving convex set in a Hilbert space, J. Diff. Eqs. 26 (1977), 347-374
16. Rockafellar, R. T., Wets, J-B.: Variational Analysis, Springer, Berlin, 1998
17. Schirotzek, W.: Nonsmooth Analysis, Springer, Berlin, 2007
18. Thibault, L.: Sweeping process with regular and nonregular sets, J. Diff. Eq. 193 (2003), 1-26 (Pubitemid 37006938)
19. Vinter, R. B.: Optimal Control, Birkhäuser, Boston, 2000.