Second-order analysis for optimal control problems with pure state constraints and mixed control-state constraints
J. Frédéric Bonnans; Audrey Hermant
Annales de l'I.H.P. Analyse non linéaire (2009)
- Volume: 26, Issue: 2, page 561-598
- ISSN: 0294-1449
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topBonnans, J. Frédéric, and 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 26.2 (2009): 561-598. <http://eudml.org/doc/78856>.
@article{Bonnans2009,
author = {Bonnans, J. Frédéric, Hermant, Audrey},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {optimal control; state constraint; mixed control-state constraint; junction conditions; necessary or sufficient second-order optimality conditions; shooting algorithm},
language = {eng},
number = {2},
pages = {561-598},
publisher = {Elsevier},
title = {Second-order analysis for optimal control problems with pure state constraints and mixed control-state constraints},
url = {http://eudml.org/doc/78856},
volume = {26},
year = {2009},
}
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
PB - Elsevier
VL - 26
IS - 2
SP - 561
EP - 598
LA - eng
KW - optimal control; state constraint; mixed control-state constraint; junction conditions; necessary or sufficient second-order optimality conditions; shooting algorithm
UR - http://eudml.org/doc/78856
ER -
References
top- [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. Zbl1167.49021
- [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. Zbl1148.49026
- [3] Bonnans J.F., Hermant A., 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. I343 (7) (2006) 473-478. Zbl1101.49020MR2267189
- [4] Bonnans J.F., Hermant A., 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. Zbl1251.49036MR2346386
- [5] Bonnans J.F., Shapiro A., Perturbation Analysis of Optimization Problems, Springer-Verlag, New York, 2000. Zbl0966.49001MR1756264
- [6] Bonnard B., Faubourg L., Launay G., Trélat E., Optimal control with state constraints and the space shuttle re-entry problem, J. Dynam. Control Systems9 (2) (2003) 155-199. Zbl1034.49014MR1968277
- [7] Bryson A.E., Denham W.F., Dreyfus S.E., Optimal programming problems with inequality constraints I: Necessary conditions for extremal solutions, AIAA J.1 (1963) 2544-2550. Zbl0142.35902MR162686
- [8] Bulirsch R., Montrone F., Pesch H.J., Abort landing in the presence of windshear as a minimax optimal control problem. I. Necessary conditions, J. Optim. Theory Appl.70 (1991) 1-23. Zbl0726.49014MR1116220
- [9] Cominetti R., Penot J.P., Tangent sets to unilateral convex sets, C. R. Acad. Sci. Paris, Sér. I321 (1995) 1631-1636. Zbl0866.49026MR1367820
- [10] Dmitruk A.V., Maximum principle for the general optimal control problem with phase and regular mixed constraints, Computational Mathematics and Modeling4 (4) (1993) 364-377. Zbl1331.49025MR1323870
- [11] Dontchev A.L., Hager W.W., Lipschitzian stability for state constrained nonlinear optimal control, SIAM J. Control Optim.36 (2) (1998) 698-718, (electronic). Zbl0917.49025MR1616530
- [12] Dontchev A.L., Hager W.W., The Euler approximation in state constrained optimal control, Math. Comp.70 (2001) 173-203. Zbl0987.49017MR1681116
- [13] Dubovitskiĭ A.Ya., Milyutin A.A., Theory of the principle of the maximum, in: Methods of the Theory of Extremal Problems in Economics, Nauka, Moscow, 1981, pp. 7-47. MR694700
- [14] Dunford N., Schwartz J., Linear Operators, vols. I and II, Interscience, New York, 1958, 1963. Zbl0084.10402MR188745
- [15] Hager W.W., Lipschitz continuity for constrained processes, SIAM J. Control Optim.17 (3) (1979) 321-338. Zbl0426.90083MR528899
- [16] Hartl R.F., Sethi S.P., Vickson R.G., A survey of the maximum principles for optimal control problems with state constraints, SIAM Rev.37 (1995) 181-218. Zbl0832.49013MR1343211
- [17] Ioffe A.D., Tihomirov V.M., Theory of Extremal Problems, North-Holland Publishing Company, Amsterdam, 1979, Russian edition: Nauka, Moscow, 1974. Zbl0407.90051MR410502
- [18] Jacobson D.H., Lele M.M., Speyer J.L., New necessary conditions of optimality for control problems with state-variable inequality constraints, J. Math. Anal. Appl.35 (1971) 255-284. Zbl0188.47203MR284905
- [19] Jittorntrum K., Solution point differentiability without strict complementarity in nonlinear programming, Math. Program.21 (1984) 127-138. Zbl0571.90080MR751247
- [20] Kawasaki H., An envelope-like effect of infinitely many inequality constraints on second order necessary conditions for minimization problems, Math. Program.41 (1988) 73-96. Zbl0661.49012MR941318
- [21] Kawasaki H., Second order necessary optimality conditions for minimizing a sup-type function, Math. Program. Ser. A49 (1990/1991) 213-229. Zbl0726.90075MR1087454
- [22] Kawasaki H., Zeidan V., Conjugate points for variational problems with equality and inequality state constraints, SIAM J. Control Optim.39 (2) (2000) 433-456, (electronic). Zbl0972.49012MR1788066
- [23] Kreindler E., Additional necessary conditions for optimal control with state-variable inequality constraints, J. Optim. Theory Appl.38 (2) (1982) 241-250. Zbl0471.49023MR686867
- [24] Malanowski K., Stability and sensitivity of solutions to nonlinear optimal control problems, J. Appl. Math. Optim.32 (1995) 111-141. Zbl0842.49020MR1332810
- [25] Malanowski K., Maurer H., Sensitivity analysis for state constrained optimal control problems, Discrete Contin. Dynam. Systems4 (1998) 241-272. Zbl0952.49022MR1617298
- [26] Malanowski K., Maurer H., Sensitivity analysis for optimal control problems subject to higher order state constraints, Ann. Oper. Res.101 (2001) 43-73. Zbl1005.49021MR1851988
- [27] Malanowski K., Maurer H., Pickenhain S., Second-order sufficient conditions for state-constrained optimal control problems, J. Optim. Theory Appl.123 (2004) 595-617. Zbl1059.49027MR2102534
- [28] H. Maurer, On the minimum principle for optimal control problems with state constraints, Schriftenreihe des Rechenzentrum 41, Universität Münster, 1979.
- [29] Milyutin A.A., The Maximum Principle in the General Problem of Optimal Control, Fizmatlit, Moscow, 2001. Zbl0998.49003
- [30] Milyutin A.A., Osmolovskii N.P., Calculus of Variations and Optimal Control, American Mathematical Society, Providence, RI, 1998. Zbl0911.49001MR1641590
- [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] Osmolovskii N.P., Higher-order necessary and sufficient conditions for Pontryagin and restricted-strong minima in an optimal control problem, Dokl. Akad. Nauk SSSR303 (5) (1988) 1052-1056. Zbl0696.49045MR985410
- [33] Páles Z., Zeidan V., First- and second-order necessary conditions for control problems with constraints, Trans. Amer. Math. Soc.346 (2) (1994) 421-453. Zbl0819.49017MR1270667
- [34] Páles Z., Zeidan V., Optimal control problems with set-valued control and state constraints, SIAM J. Optim.14 (2003) 334-358, (electronic). Zbl1041.49025MR2048167
- [35] Páles Z., Zeidan V., Strong local optimality conditions for state constrained control problems, J. Global Optim.28 (3–4) (2004) 363-377. Zbl1152.49310MR2074794
- [36] Robinson S.M., Strongly regular generalized equations, Math. Oper. Res.5 (1980) 43-62. Zbl0437.90094MR561153
Citations in EuDML Documents
top- Nikolai P. Osmolovskii, Second-order sufficient optimality conditions for control problems with linearly independent gradients of control constraints
- Nikolai P. Osmolovskii, Second-order sufficient optimality conditions for control problems with linearly independent gradients of control constraints
- J. Frédéric Bonnans, Xavier Dupuis, Laurent Pfeiffer, Second-order sufficient conditions for strong solutions to optimal control problems
- Joseph Frédéric Bonnans, Audrey Hermant, Stability and sensitivity analysis for optimal control problems with a first-order state constraint and application to continuation methods
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