Cernea, Aurelian; Georgescu, Carmina Necessary optimality conditions for differential-difference inclusions with state constraints. (English) Zbl 1124.49018 J. Math. Anal. Appl. 334, No. 1, 43-53 (2007). Summary: We consider the Mayer optimal control problem with dynamics given by a nonconvex differential-difference inclusion, whose trajectories are constrained to a closed set. Necessary optimality conditions in the form of the maximum principle are obtained. Cited in 5 Documents MSC: 49K24 Optimal control problems with differential inclusions (nec./ suff.) (MSC2000) 49K30 Optimality conditions for solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.) Keywords:differential-difference inclusions; maximum principle; state constraints; variational inclusions PDFBibTeX XMLCite \textit{A. Cernea} and \textit{C. Georgescu}, J. Math. Anal. Appl. 334, No. 1, 43--53 (2007; Zbl 1124.49018) Full Text: DOI References: [1] Aubin, J. P.; Frankowska, H., Set-Valued Analysis (1990), Birkhäuser: Birkhäuser Boston [2] Borwein, J., Weak tangent cones and optimization in a Banach space, SIAM J. Control Optim., 3, 512-522 (1978) · Zbl 0383.90109 [3] Cernea, A., Conditions nécessaires d’optimalité pour les solutions d’une inclusion differentielle avec contraintes d’état, Bull. Acad. Polon. Sci. Math., 43, 169-173 (1995) · Zbl 0829.49022 [4] Cernea, A., Necessary optimality conditions for a class of differential inclusions with state constraints, Rev. Roumaine Math. Pures Appl., 47, 295-304 (2002) · Zbl 1094.49021 [5] Cernea, A., Second-order necessary conditions for differential-difference inclusions, Nonlinear Anal., 62, 963-974 (2005) · Zbl 1114.49022 [6] Cernea, A., Derived cones to reachable sets of differential-difference inclusions, Nonlinear Anal. Forum, 11, 1-13 (2006) · Zbl 1131.34047 [7] Cernea, A.; Frankowska, H., A connection between the maximum principle and dynamic programming for constrained control problems, SIAM J. Control Optim., 44, 673-703 (2005) · Zbl 1085.49032 [8] Cernea, A.; Georgescu, C., Controllability and extremality for differential-difference inclusions, Comm. Appl. Nonlinear Anal., 14, 1-12 (2007) · Zbl 1136.34060 [9] Clarke, F. H.; Watkins, G. G., Necessary conditions, controllability and the value function for differential-difference inclusions, Nonlinear Anal., 10, 1155-1179 (1986) · Zbl 0609.49013 [10] Frankowska, H., The maximum principle for an optimal solution to a differential inclusion with end points constraints, SIAM J. Control Optim., 25, 145-157 (1987) · Zbl 0614.49017 [11] Frankowska, H., Contingent cones to reachable sets of control systems, SIAM J. Control Optim., 27, 170-198 (1989) · Zbl 0671.49030 [12] Minchenko, L. I., Necessary optimality conditions for differential-difference inclusions, Nonlinear Anal., 35, 307-322 (1999) · Zbl 0926.49015 [13] Minchenko, L. I.; Teslyuk, V. N., On controllability of convex processes with delay, J. Optim. Theory Appl., 74, 191-197 (1992) · Zbl 0827.49015 [14] Minchenko, L. I.; Teslyuk, V. N., Local controllability of generalized delay differential equations, Differ. Equ., 32, 1630-1636 (1996) · Zbl 0882.49006 [15] Minchenko, L. I.; Volosevich, A. A., Value function and necessary conditions in optimal control problems for differential-difference inclusions, Nonlinear Anal., 53, 407-424 (2003) · Zbl 1030.49024 [16] Mirică, Şt., New proof and some generalizations of the minimum principle in optimal control, J. Optim. Theory Appl., 74, 487-508 (1992) [17] Mordukhovich, B. S., Optimal control of difference, differential and differential-difference inclusions, J. Math. Sci., 100, 2613-2632 (2000) · Zbl 0966.49018 [18] Mordukhovich, B. S.; Trubnik, R., Stability of discrete approximations and necessary optimality conditions for delay-differential inclusions, Ann. Oper. Res., 101, 149-170 (2001) · Zbl 1006.49016 [19] Mordukhovich, B. S.; Wang, L., Optimal control of neutral functional-differential inclusions, SIAM J. Control Optim., 43, 111-136 (2004) · Zbl 1070.49016 [20] Mordukhovich, B. S.; Wang, L., Optimal control of delay systems with differential and algebraic dynamic constraints, ESAIM Control Optim. Calc. Var., 11, 285-309 (2005) · Zbl 1081.49017 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.