Necessary optimality conditions for differential-difference inclusions with state constraints

Journal of Mathematical Analysis and Applications

Volumn 334, Issue 1, 2007, Pages 43-53

  Cernea, Aurelian ^a   Georgescu, Carmina ^b  

^a UNIVERSITY OF BUCHAREST   (Romania)

^b UNIVERSITY POLITEHNICA OF BUCHAREST   (Romania)

Author keywords

Differential difference inclusions; Maximum principle; State constraints; Variational inclusions

Indexed keywords

EID: 34249281984     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2006.12.020     Document Type: Article

References (20)

1. Aubin J.P., and Frankowska H. Set-Valued Analysis (1990), Birkhäuser, Boston
2. Borwein J. Weak tangent cones and optimization in a Banach space. SIAM J. Control Optim. 3 (1978) 512-522
3. Cernea A. Conditions nécessaires d'optimalité pour les solutions d'une inclusion differentielle avec contraintes d'état. Bull. Acad. Polon. Sci. Math. 43 (1995) 169-173
4. Cernea A. Necessary optimality conditions for a class of differential inclusions with state constraints. Rev. Roumaine Math. Pures Appl. 47 (2002) 295-304
5. Cernea A. Second-order necessary conditions for differential-difference inclusions. Nonlinear Anal. 62 (2005) 963-974
6. Cernea A. Derived cones to reachable sets of differential-difference inclusions. Nonlinear Anal. Forum 11 (2006) 1-13
7. Cernea A., and Frankowska H. A connection between the maximum principle and dynamic programming for constrained control problems. SIAM J. Control Optim. 44 (2005) 673-703
8. Cernea A., and Georgescu C. Controllability and extremality for differential-difference inclusions. Comm. Appl. Nonlinear Anal. 14 (2007) 1-12
9. Clarke F.H., and Watkins G.G. Necessary conditions, controllability and the value function for differential-difference inclusions. Nonlinear Anal. 10 (1986) 1155-1179
10. Frankowska H. The maximum principle for an optimal solution to a differential inclusion with end points constraints. SIAM J. Control Optim. 25 (1987) 145-157
11. Frankowska H. Contingent cones to reachable sets of control systems. SIAM J. Control Optim. 27 (1989) 170-198
12. Minchenko L.I. Necessary optimality conditions for differential-difference inclusions. Nonlinear Anal. 35 (1999) 307-322
13. Minchenko L.I., and Teslyuk V.N. On controllability of convex processes with delay. J. Optim. Theory Appl. 74 (1992) 191-197
14. Minchenko L.I., and Teslyuk V.N. Local controllability of generalized delay differential equations. Differ. Equ. 32 (1996) 1630-1636
15. Minchenko L.I., and Volosevich A.A. Value function and necessary conditions in optimal control problems for differential-difference inclusions. Nonlinear Anal. 53 (2003) 407-424
16. Miricǎ St. New proof and some generalizations of the minimum principle in optimal control. J. Optim. Theory Appl. 74 (1992) 487-508
17. Mordukhovich B.S. Optimal control of difference, differential and differential-difference inclusions. J. Math. Sci. 100 (2000) 2613-2632
18. Mordukhovich B.S., and Trubnik R. Stability of discrete approximations and necessary optimality conditions for delay-differential inclusions. Ann. Oper. Res. 101 (2001) 149-170
19. Mordukhovich B.S., and Wang L. Optimal control of neutral functional-differential inclusions. SIAM J. Control Optim. 43 (2004) 111-136
20. Mordukhovich B.S., and Wang L. Optimal control of delay systems with differential and algebraic dynamic constraints. ESAIM Control Optim. Calc. Var. 11 (2005) 285-309