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.
@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 = {https://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  - https://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 https://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. https://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] 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. I 343 (7) (2006) 473-478. | MR | Zbl

[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. | MR

[5] Bonnans J. F., Shapiro A., Perturbation Analysis of Optimization Problems, Springer-Verlag, New York, 2000. | MR | Zbl

[6] Bonnard B., Faubourg L., Launay G., Trélat E., Optimal Control With State Constraints and the Space Shuttle Re-Entry Problem, J. Dynam. Control Systems 9 (2) (2003) 155-199. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[9] Cominetti R., Penot J. P., Tangent Sets to Unilateral Convex Sets, C. R. Acad. Sci. Paris, Sér. I 321 (1995) 1631-1636. | MR | Zbl

[10] Dmitruk A. V., 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] Dontchev A. L., Hager W. W., Lipschitzian Stability for State Constrained Nonlinear Optimal Control, SIAM J. Control Optim. 36 (2) (1998) 698-718, (electronic). | MR | Zbl

[12] Dontchev A. L., Hager W. W., The Euler Approximation in State Constrained Optimal Control, Math. Comp. 70 (2001) 173-203. | MR | Zbl

[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. | MR

[14] Dunford N., Schwartz J., Linear Operators, Vols. I and II, Interscience, New York, 1958, 1963. | MR | Zbl

[15] Hager W. W., Lipschitz Continuity for Constrained Processes, SIAM J. Control Optim. 17 (3) (1979) 321-338. | MR | Zbl

[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. | MR | Zbl

[17] Ioffe A. D., Tihomirov V. M., Theory of Extremal Problems, North-Holland Publishing Company, Amsterdam, 1979, Russian edition: Nauka, Moscow, 1974. | MR | Zbl

[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. | MR | Zbl

[19] Jittorntrum K., Solution Point Differentiability Without Strict Complementarity in Nonlinear Programming, Math. Program. 21 (1984) 127-138. | MR | Zbl

[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. | MR | Zbl

[21] Kawasaki H., Second Order Necessary Optimality Conditions for Minimizing a Sup-Type Function, Math. Program. Ser. A 49 (1990/1991) 213-229. | MR | Zbl

[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). | MR | Zbl

[23] Kreindler E., Additional Necessary Conditions for Optimal Control With State-Variable Inequality Constraints, J. Optim. Theory Appl. 38 (2) (1982) 241-250. | MR | Zbl

[24] Malanowski K., Stability and Sensitivity of Solutions to Nonlinear Optimal Control Problems, J. Appl. Math. Optim. 32 (1995) 111-141. | MR | Zbl

[25] Malanowski K., Maurer H., Sensitivity Analysis for State Constrained Optimal Control Problems, Discrete Contin. Dynam. Systems 4 (1998) 241-272. | MR | Zbl

[26] Malanowski K., Maurer H., Sensitivity Analysis for Optimal Control Problems Subject to Higher Order State Constraints, Ann. Oper. Res. 101 (2001) 43-73. | MR | Zbl

[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. | MR | Zbl

[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. | Zbl

[30] Milyutin A. A., Osmolovskii N. P., 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] Osmolovskii N. P., 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] Páles Z., Zeidan V., First- and Second-Order Necessary Conditions for Control Problems With Constraints, Trans. Amer. Math. Soc. 346 (2) (1994) 421-453. | MR | Zbl

[34] Páles Z., Zeidan V., Optimal Control Problems With Set-Valued Control and State Constraints, SIAM J. Optim. 14 (2003) 334-358, (electronic). | MR | Zbl

[35] Páles Z., Zeidan V., Strong Local Optimality Conditions for State Constrained Control Problems, J. Global Optim. 28 (3-4) (2004) 363-377. | MR | Zbl

[36] Robinson S. M., Strongly Regular Generalized Equations, Math. Oper. Res. 5 (1980) 43-62. | MR | Zbl

  • Malisani, Paul Interior point methods in optimal control, ESAIM: Control, Optimisation and Calculus of Variations, Volume 30 (2024), p. 59 | DOI:10.1051/cocv/2024049
  • Casas, Eduardo; Mateos, Mariano; Rösch, Arnd New second order sufficient optimality conditions for state constrained parabolic control problems, Optimization (2024), p. 1 | DOI:10.1080/02331934.2024.2314242
  • Caillau, Jean-Baptiste; Ferretti, Roberto; Trélat, Emmanuel; Zidani, Hasnaa An algorithmic guide for finite-dimensional optimal control problems, Numerical Control: Part B, Volume 24 (2023), p. 559 | DOI:10.1016/bs.hna.2022.11.006
  • Bonnans, J. Frédéric; Gianatti, Justina; Pfeiffer, Laurent A Lagrangian Approach for Aggregative Mean Field Games of Controls with Mixed and Final Constraints, SIAM Journal on Control and Optimization, Volume 61 (2023) no. 1, p. 105 | DOI:10.1137/21m1407720
  • Malisani, Paul Interior Point Methods in Optimal Control Problems of Affine Systems: Convergence Results and Solving Algorithms, SIAM Journal on Control and Optimization, Volume 61 (2023) no. 6, p. 3390 | DOI:10.1137/23m1561233
  • Osmolovskii, Nikolai P. A second-order sufficient condition for a weak local minimum in an optimal control problem with an inequality control constraint, Control and Cybernetics, Volume 51 (2022) no. 2, p. 151 | DOI:10.2478/candc-2022-0012
  • He, Suqin; Hu, Chuxiong; Lin, Shize; Zhu, Yu; Tomizuka, Masayoshi Real-time time-optimal continuous multi-axis trajectory planning using the trajectory index coordination method, ISA Transactions, Volume 131 (2022), p. 639 | DOI:10.1016/j.isatra.2022.05.016
  • Becerril, Jorge; Hermosilla, Cristopher Optimality Conditions for Linear-Convex Optimal Control Problems with Mixed Constraints, Journal of Optimization Theory and Applications, Volume 194 (2022) no. 3, p. 795 | DOI:10.1007/s10957-022-02049-4
  • Dmitruk, Andrei; Osmolovskii, Nikolai Local Minimum Principle for an Optimal Control Problem with a Nonregular Mixed Constraint, SIAM Journal on Control and Optimization, Volume 60 (2022) no. 4, p. 1919 | DOI:10.1137/21m1411469
  • Christof, Constantin; Wachsmuth, Gerd On second-order optimality conditions for optimal control problems governed by the obstacle problem, Optimization, Volume 70 (2021) no. 10, p. 2247 | DOI:10.1080/02331934.2020.1778686
  • Giang, N. B.; Tuan, N. Q.; Son, N. H. Second-order optimality conditions and regularity of Lagrange multipliers for mixed optimal control problems, Positivity, Volume 25 (2021) no. 3, p. 911 | DOI:10.1007/s11117-020-00793-3
  • Aronna, M. Soledad; Bonnans, J. Frédéric; Kröner, Axel State-Constrained Control-Affine Parabolic Problems I: First and Second Order Necessary Optimality Conditions, Set-Valued and Variational Analysis, Volume 29 (2021) no. 2, p. 383 | DOI:10.1007/s11228-020-00560-2
  • Sánchez, Marcelino; Delprat, Sébastien; Hofman, Theo Energy management of hybrid vehicles with state constraints: A penalty and implicit Hamiltonian minimization approach, Applied Energy, Volume 260 (2020), p. 114149 | DOI:10.1016/j.apenergy.2019.114149
  • Bayen, Terence; Pfeiffer, Laurent, 2019 IEEE 58th Conference on Decision and Control (CDC) (2019), p. 1480 | DOI:10.1109/cdc40024.2019.9029314
  • Cui, Qing; Deng, Li; Zhang, Xu Second order optimality conditions for optimal control problems on Riemannian manifolds, ESAIM: Control, Optimisation and Calculus of Variations, Volume 25 (2019), p. 35 | DOI:10.1051/cocv/2018028
  • Martens, Björn; Gerdts, Matthias Convergence Analysis of the Implicit Euler-discretization and Sufficient Conditions for Optimal Control Problems Subject to Index-one Differential-algebraic Equations, Set-Valued and Variational Analysis, Volume 27 (2019) no. 2, p. 405 | DOI:10.1007/s11228-018-0471-x
  • Frankowska, Hélène; Osmolovskii, Nikolai P. Strong Local Minimizers in Optimal Control Problems with State Constraints: Second-Order Necessary Conditions, SIAM Journal on Control and Optimization, Volume 56 (2018) no. 3, p. 2353 | DOI:10.1137/17m1160604
  • Zhang, Haisen; Zhang, Xu Second-Order Necessary Conditions for Stochastic Optimal Control Problems, SIAM Review, Volume 60 (2018) no. 1, p. 139 | DOI:10.1137/17m1148773
  • Frego, Marco; Bertolazzi, Enrico; Biral, Francesco; Fontanelli, Daniele; Palopoli, Luigi Semi-analytical minimum time solutions with velocity constraints for trajectory following of vehicles, Automatica, Volume 86 (2017), p. 18 | DOI:10.1016/j.automatica.2017.08.020
  • Zhang, Haisen; Zhang, Xu Pointwise Second-Order Necessary Conditions for Stochastic Optimal Controls, Part II: The General Case, SIAM Journal on Control and Optimization, Volume 55 (2017) no. 5, p. 2841 | DOI:10.1137/15m1045478
  • Bonnans, J. Frédéric; Festa, Adriano Error Estimates for the Euler Discretization of an Optimal Control Problem with First-Order State Constraints, SIAM Journal on Numerical Analysis, Volume 55 (2017) no. 2, p. 445 | DOI:10.1137/140999621
  • Kien, B. T.; Nhu, V. H.; Son, N. H. Second-Order Optimality Conditions for a Semilinear Elliptic Optimal Control Problem with Mixed Pointwise Constraints, Set-Valued and Variational Analysis, Volume 25 (2017) no. 1, p. 177 | DOI:10.1007/s11228-016-0373-8
  • Deng, Li, 2016 35th Chinese Control Conference (CCC) (2016), p. 1362 | DOI:10.1109/chicc.2016.7553279
  • Son, N. H.; Kien, B. T.; Rösch, A. Second-Order Optimality Conditions for Boundary Control Problems with Mixed Pointwise Constraints, SIAM Journal on Optimization, Volume 26 (2016) no. 3, p. 1912 | DOI:10.1137/15m1033629
  • Cui, Qing; Deng, Li; Zhang, Xu Pointwise second-order necessary conditions for optimal control problems evolved on Riemannian manifolds, Comptes Rendus. Mathématique, Volume 354 (2015) no. 2, p. 191 | DOI:10.1016/j.crma.2015.09.032
  • Kien, B. T.; Nhu, V. H.; Rösch, A. Second-Order Necessary Optimality Conditions for a Class of Optimal Control Problems Governed by Partial Differential Equations with Pure State Constraints, Journal of Optimization Theory and Applications, Volume 165 (2015) no. 1, p. 30 | DOI:10.1007/s10957-014-0628-1
  • Frédéric Bonnans, J.; Dupuis, Xavier; Pfeiffer, Laurent Second-order sufficient conditions for strong solutions to optimal control problems, ESAIM: Control, Optimisation and Calculus of Variations, Volume 20 (2014) no. 3, p. 704 | DOI:10.1051/cocv/2013080
  • Aftalion, Amandine; Bonnans, J. Frédéric Optimization of Running Strategies Based on Anaerobic Energy and Variations of Velocity, SIAM Journal on Applied Mathematics, Volume 74 (2014) no. 5, p. 1615 | DOI:10.1137/130932697
  • Hoehener, Daniel Variational Approach to Second-Order Sufficient Optimality Conditions in Optimal Control, SIAM Journal on Control and Optimization, Volume 52 (2014) no. 2, p. 861 | DOI:10.1137/130912803
  • Bonnans, J. Frédéric; Dupuis, Xavier; Pfeiffer, Laurent Second-Order Necessary Conditions in Pontryagin Form for Optimal Control Problems, SIAM Journal on Control and Optimization, Volume 52 (2014) no. 6, p. 3887 | DOI:10.1137/130923452
  • Hoehener, Daniel, 52nd IEEE Conference on Decision and Control (2013), p. 544 | DOI:10.1109/cdc.2013.6759938
  • Hoehener, Daniel Feasible Perturbations of Control Systems with Pure State Constraints and Applications to Second-Order Optimality Conditions, Applied Mathematics Optimization, Volume 68 (2013) no. 2, p. 219 | DOI:10.1007/s00245-013-9204-6
  • Bonnans, J. Frédéric The shooting approach to optimal control problems, IFAC Proceedings Volumes, Volume 46 (2013) no. 11, p. 281 | DOI:10.3182/20130703-3-fr-4038.00158
  • Fontes, Fernando A.C.C.; Lopes, Sofia O. Normal forms of necessary conditions for dynamic optimization problems with pathwise inequality constraints, Journal of Mathematical Analysis and Applications, Volume 399 (2013) no. 1, p. 27 | DOI:10.1016/j.jmaa.2012.09.049
  • Bonnans, J. Frédéric; de la Vega, Constanza; Dupuis, Xavier First- and Second-Order Optimality Conditions for Optimal Control Problems of State Constrained Integral Equations, Journal of Optimization Theory and Applications, Volume 159 (2013) no. 1, p. 1 | DOI:10.1007/s10957-013-0299-3
  • Osmolovskii, Nikolai P. Second-order sufficient optimality conditions for control problems with linearly independent gradients of control constraints, ESAIM: Control, Optimisation and Calculus of Variations, Volume 18 (2012) no. 2, p. 452 | DOI:10.1051/cocv/2011101
  • Osmolovskii, N. P. Necessary quadratic conditions of extremum for discontinuous controls in optimal control problems with mixed constraints, Journal of Mathematical Sciences, Volume 183 (2012) no. 4, p. 435 | DOI:10.1007/s10958-012-0824-1
  • Trélat, E. Optimal Control and Applications to Aerospace: Some Results and Challenges, Journal of Optimization Theory and Applications, Volume 154 (2012) no. 3, p. 713 | DOI:10.1007/s10957-012-0050-5
  • Hoehener, Daniel Variational Approach to Second-Order Optimality Conditions for Control Problems with Pure State Constraints, SIAM Journal on Control and Optimization, Volume 50 (2012) no. 3, p. 1139 | DOI:10.1137/110828320
  • do Rosário de Pinho, Maria; Shvartsman, Ilya Lipschitz continuity of optimal control and Lagrange multipliers in a problem with mixed and pure state constraints, Discrete Continuous Dynamical Systems - A, Volume 29 (2011) no. 2, p. 505 | DOI:10.3934/dcds.2011.29.505
  • Osmolovskii, N. P. Sufficient quadratic conditions of extremum for discontinuous controls in optimal control problems with mixed constraints, Journal of Mathematical Sciences, Volume 173 (2011) no. 1, p. 1 | DOI:10.1007/s10958-011-0233-x
  • Hermant, Audrey Optimal control of the atmospheric reentry of a space shuttle by an homotopy method, Optimal Control Applications and Methods, Volume 32 (2011) no. 6, p. 627 | DOI:10.1002/oca.961
  • Shvartsman, Ilya, 49th IEEE Conference on Decision and Control (CDC) (2010), p. 6657 | DOI:10.1109/cdc.2010.5716970
  • Hermant, Audrey Homotopy Algorithm for Optimal Control Problems with a Second-order State Constraint, Applied Mathematics and Optimization, Volume 61 (2010) no. 1, p. 85 | DOI:10.1007/s00245-009-9076-y
  • Bonnans, J. Frédéric; Jaisson, Pascal Optimal Control of a Parabolic Equation with Time-Dependent State Constraints, SIAM Journal on Control and Optimization, Volume 48 (2010) no. 7, p. 4550 | DOI:10.1137/080744608
  • Bonnans, Joseph Frédéric; Sánchez Fernández de la Vega, Constanza Optimal Control of State Constrained Integral Equations, Set-Valued and Variational Analysis, Volume 18 (2010) no. 3-4, p. 307 | DOI:10.1007/s11228-010-0154-8
  • Hermant, Audrey Stability Analysis of Optimal Control Problems with a Second-Order State Constraint, SIAM Journal on Optimization, Volume 20 (2009) no. 1, p. 104 | DOI:10.1137/070707993

Cité par 47 documents. Sources : Crossref