@article{AIHPC_2009__26_2_561_0, author = {Bonnans, J. Fr\'eD\'eRic and Hermant, Audrey}, title = {Second-Order {Analysis} for {Optimal} {Control} {Problems} {With} {Pure} {State} {Constraints} and {Mixed} {Control-State} {Constraints}}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {561--598}, publisher = {Elsevier}, volume = {26}, number = {2}, year = {2009}, doi = {10.1016/j.anihpc.2007.12.002}, mrnumber = {2504044}, zbl = {1158.49023}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.anihpc.2007.12.002/} }
TY - JOUR AU - Bonnans, J. FréDéRic AU - Hermant, Audrey TI - Second-Order Analysis for Optimal Control Problems With Pure State Constraints and Mixed Control-State Constraints JO - Annales de l'I.H.P. Analyse non linéaire PY - 2009 SP - 561 EP - 598 VL - 26 IS - 2 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2007.12.002/ DO - 10.1016/j.anihpc.2007.12.002 LA - en ID - AIHPC_2009__26_2_561_0 ER -
%0 Journal Article %A Bonnans, J. FréDéRic %A Hermant, Audrey %T Second-Order Analysis for Optimal Control Problems With Pure State Constraints and Mixed Control-State Constraints %J Annales de l'I.H.P. Analyse non linéaire %D 2009 %P 561-598 %V 26 %N 2 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2007.12.002/ %R 10.1016/j.anihpc.2007.12.002 %G en %F AIHPC_2009__26_2_561_0
Bonnans, J. FréDéRic; Hermant, Audrey. Second-Order Analysis for Optimal Control Problems With Pure State Constraints and Mixed Control-State Constraints. Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) no. 2, pp. 561-598. doi : 10.1016/j.anihpc.2007.12.002. http://www.numdam.org/articles/10.1016/j.anihpc.2007.12.002/
[1] J.F. Bonnans, A. Hermant, No gap second order optimality conditions for optimal control problems with a single state constraint and control. INRIA Research Report 5837, Mathematical Programming, in press. Online first doi 10.1007/s10107-007-0167-8.
[2] J.F. Bonnans, A. Hermant, Stability and sensitivity analysis for optimal control problems with a first-order state constraint, ESAIM Control Optim. Calc. Var., E-first DOI 10.1051/cocv:2008016. | Numdam | Zbl
[3] Conditions D'optimalité Du Second Ordre Nécessaires Ou Suffisantes Pour Les Problèmes De Commande Optimale Avec Une Contrainte Sur L'état Et Une Commande Scalaires, C. R. Math. Acad. Sci. Paris, Ser. I 343 (7) (2006) 473-478. | MR | Zbl
, ,[4] Well-Posedness of the Shooting Algorithm for State Constrained Optimal Control Problems With a Single Constraint and Control, SIAM J. Control Optim. 46 (4) (2007) 1398-1430. | MR
, ,[5] Perturbation Analysis of Optimization Problems, Springer-Verlag, New York, 2000. | MR | Zbl
, ,[6] Optimal Control With State Constraints and the Space Shuttle Re-Entry Problem, J. Dynam. Control Systems 9 (2) (2003) 155-199. | MR | Zbl
, , , ,[7] Optimal Programming Problems With Inequality Constraints I: Necessary Conditions for Extremal Solutions, AIAA J. 1 (1963) 2544-2550. | MR | Zbl
, , ,[8] Abort Landing in the Presence of Windshear as a Minimax Optimal Control Problem. I. Necessary Conditions, J. Optim. Theory Appl. 70 (1991) 1-23. | MR | Zbl
, , ,[9] Tangent Sets to Unilateral Convex Sets, C. R. Acad. Sci. Paris, Sér. I 321 (1995) 1631-1636. | MR | Zbl
, ,[10] Maximum Principle for the General Optimal Control Problem With Phase and Regular Mixed Constraints, Computational Mathematics and Modeling 4 (4) (1993) 364-377. | MR
,[11] Lipschitzian Stability for State Constrained Nonlinear Optimal Control, SIAM J. Control Optim. 36 (2) (1998) 698-718, (electronic). | MR | Zbl
, ,[12] The Euler Approximation in State Constrained Optimal Control, Math. Comp. 70 (2001) 173-203. | MR | Zbl
, ,[13] Theory of the Principle of the Maximum, in: Methods of the Theory of Extremal Problems in Economics, Nauka, Moscow, 1981, pp. 7-47. | MR
, ,[14] Linear Operators, Vols. I and II, Interscience, New York, 1958, 1963. | MR | Zbl
, ,[15] Lipschitz Continuity for Constrained Processes, SIAM J. Control Optim. 17 (3) (1979) 321-338. | MR | Zbl
,[16] A Survey of the Maximum Principles for Optimal Control Problems With State Constraints, SIAM Rev. 37 (1995) 181-218. | MR | Zbl
, , ,[17] Theory of Extremal Problems, North-Holland Publishing Company, Amsterdam, 1979, Russian edition: Nauka, Moscow, 1974. | MR | Zbl
, ,[18] New Necessary Conditions of Optimality for Control Problems With State-Variable Inequality Constraints, J. Math. Anal. Appl. 35 (1971) 255-284. | MR | Zbl
, , ,[19] Solution Point Differentiability Without Strict Complementarity in Nonlinear Programming, Math. Program. 21 (1984) 127-138. | MR | Zbl
,[20] An Envelope-Like Effect of Infinitely Many Inequality Constraints on Second Order Necessary Conditions for Minimization Problems, Math. Program. 41 (1988) 73-96. | MR | Zbl
,[21] Second Order Necessary Optimality Conditions for Minimizing a Sup-Type Function, Math. Program. Ser. A 49 (1990/1991) 213-229. | MR | Zbl
,[22] Conjugate Points for Variational Problems With Equality and Inequality State Constraints, SIAM J. Control Optim. 39 (2) (2000) 433-456, (electronic). | MR | Zbl
, ,[23] Additional Necessary Conditions for Optimal Control With State-Variable Inequality Constraints, J. Optim. Theory Appl. 38 (2) (1982) 241-250. | MR | Zbl
,[24] Stability and Sensitivity of Solutions to Nonlinear Optimal Control Problems, J. Appl. Math. Optim. 32 (1995) 111-141. | MR | Zbl
,[25] Sensitivity Analysis for State Constrained Optimal Control Problems, Discrete Contin. Dynam. Systems 4 (1998) 241-272. | MR | Zbl
, ,[26] Sensitivity Analysis for Optimal Control Problems Subject to Higher Order State Constraints, Ann. Oper. Res. 101 (2001) 43-73. | MR | Zbl
, ,[27] Second-Order Sufficient Conditions for State-Constrained Optimal Control Problems, J. Optim. Theory Appl. 123 (2004) 595-617. | MR | Zbl
, , ,[28] H. Maurer, On the minimum principle for optimal control problems with state constraints, Schriftenreihe des Rechenzentrum 41, Universität Münster, 1979.
[29] The Maximum Principle in the General Problem of Optimal Control, Fizmatlit, Moscow, 2001. | Zbl
,[30] Calculus of Variations and Optimal Control, American Mathematical Society, Providence, RI, 1998. | MR | Zbl
, ,[31] H.J. Oberle, W. Grimm, Bndsco - a program for the numerical solution of optimal control problems, Technical report, Report No. 515, Institut for Flight Systems Dynamics, Oberpfaffenhofen, German Aerospace Research Establishment DLR, 1989.
[32] Higher-Order Necessary and Sufficient Conditions for Pontryagin and Restricted-Strong Minima in an Optimal Control Problem, Dokl. Akad. Nauk SSSR 303 (5) (1988) 1052-1056. | MR | Zbl
,[33] First- and Second-Order Necessary Conditions for Control Problems With Constraints, Trans. Amer. Math. Soc. 346 (2) (1994) 421-453. | MR | Zbl
, ,[34] Optimal Control Problems With Set-Valued Control and State Constraints, SIAM J. Optim. 14 (2003) 334-358, (electronic). | MR | Zbl
, ,[35] Strong Local Optimality Conditions for State Constrained Control Problems, J. Global Optim. 28 (3-4) (2004) 363-377. | MR | Zbl
, ,[36] Strongly Regular Generalized Equations, Math. Oper. Res. 5 (1980) 43-62. | MR | Zbl
,Cité par Sources :