Stability and sensitivity analysis for optimal control problems. A survey
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 16 (2010) no. 5, pp. 278-288
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

The general methodology used in stability and sensitivity analysis for optimization problems is outlined, with emphasis on similarities and differences between equality and cone-constrained problems, respectively. The application of that methodology to nonlinear optimal control problems subject to control and state constraints is shortly described.
Keywords: stability and sensitivity analysis, optimal control, ordinary differential equations, control and state constraints.
@article{TIMM_2010_16_5_a31,
     author = {K. Malanowski},
     title = {Stability and sensitivity analysis for optimal control problems. {A} survey},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {278--288},
     year = {2010},
     volume = {16},
     number = {5},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2010_16_5_a31/}
}
TY  - JOUR
AU  - K. Malanowski
TI  - Stability and sensitivity analysis for optimal control problems. A survey
JO  - Trudy Instituta matematiki i mehaniki
PY  - 2010
SP  - 278
EP  - 288
VL  - 16
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/TIMM_2010_16_5_a31/
LA  - en
ID  - TIMM_2010_16_5_a31
ER  - 
%0 Journal Article
%A K. Malanowski
%T Stability and sensitivity analysis for optimal control problems. A survey
%J Trudy Instituta matematiki i mehaniki
%D 2010
%P 278-288
%V 16
%N 5
%U http://geodesic.mathdoc.fr/item/TIMM_2010_16_5_a31/
%G en
%F TIMM_2010_16_5_a31
K. Malanowski. Stability and sensitivity analysis for optimal control problems. A survey. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 16 (2010) no. 5, pp. 278-288. http://geodesic.mathdoc.fr/item/TIMM_2010_16_5_a31/

[1] Bonnans J.-F., Shapiro A., Perturbed analysis of optimization problems, Springer-Verlag, New York, 2000 | MR | Zbl

[2] Dontchev A. L., “Implicit function theorems for generalized equations”, Math. Program., 70 (1995), 91–106 | MR | Zbl

[3] Dontchev A. L., Hager W. W., Poor A. B., Yang B., “Optimality, stability and convergence in nonlinear control”, Appl. Math. Optim., 31 (1995), 297–326 | DOI | MR | Zbl

[4] Dontchev A. L., Hager W. W., “Lipschitzian stability for state constrained nonlinear optimal control”, SIAM J. Control Optim., 36 (1998), 698–718 | DOI | MR | Zbl

[5] Felgenhauer U., “On stability of bang-bang type controls”, SIAM J. Control Optim., 41 (2003), 1843–1867 | DOI | MR | Zbl

[6] Hartl R. F., Sethi S. P., Vickson R. G., “A survey of the maximum principle for optimal control problems with state constraints”, SIAM Review, 37 (1995), 181–212 | DOI | MR

[7] Haraux A., “How to differentiate the projection on a convex set in Hilbert space. Some applications to variational inequalities”, J. Math. Soc. Japan, 29 (1977), 615–631 | DOI | MR | Zbl

[8] Hermant A., “Stability analysis of optimal control problems with a second order state constraint”, SIAM J. Optimization, 20 (2009), 104–129 | DOI | MR | Zbl

[9] Malanowski K., “Stability and sensitivity analysis for optimal control problems with control-state constraints”, Dissertationes Math., 394 (2001), 1–51 | DOI | MR | Zbl

[10] Malanowski K., “On normality of Lagrange multipliers for state constrained optimal control problems”, Optimization, 52 (2003), 75–91 | DOI | MR | Zbl

[11] Malanowski K., “Stability analysis for nonlinear optimal control problems subject to state constraints”, SIAM J. Optim., 18 (2007), 926–945 | DOI | MR | Zbl

[12] Malanowski K., “Stability analysis for control and state constrained optimal control problems”, Advances in Dynamics and Control Theory Methods and Applications, Cambridge Scientific Publisher, Cambridge, 2009, 45–57

[13] Robinson S. M., “Strongly regular generalized equations”, Math. Oper. Res., 5 (1980), 43–62 | DOI | MR | Zbl

[14] Robinson S. M., “An implicit function theorem for a class of nonsmooth functions”, Math. Oper. Res., 16 (1991), 292–309 | DOI | MR | Zbl