Stability and local growth near bounded-strong optimal controls

IFIP Advances in Information and Communication Technology

Volumn 130, Issue , 2003, Pages 213-227

  Felgenhauer, Ursula ^a  

^a Technical University of Cottbus   (Germany)

Author keywords

Constrained control problems; Stability; Sufficient optimality conditions

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; INFORMATION TECHNOLOGY;

CONSTRAINED CONTROLS; CONSTRAINED OPTIMAL CONTROL PROBLEMS; CONTINUOUS CONTROL; DISCONTINUOUS CONTROL; MINIMIZING SEQUENCE; OPTIMALITY CONDITIONS; OPTIMALITY CRITERIA; SUFFICIENT OPTIMALITY CONDITIONS;

OPTIMAL CONTROL SYSTEMS;

EID: 84904363341     PISSN: 18684238     EISSN: None     Source Type: Book Series    
DOI: None     Document Type: Conference Paper

References (21)

1. Dontchev, A. L., and Hager, W. W. Lipschitzian stability in nonlinear control and optimization, SIAM J. Control and Optimization, 31:569-603, 1993.
2. Dontchev, A. L., and Hager, W. W. The Euler approximation in state constrained optimal control, Math. Comp., 70(233):173-203, 2001.
3. Dontchev, A. L., and Malanowski, K. A characterization of Lipschitzian stability in optimal control, In Joffe et al.[8], pages 62-76.
4. Felgenhauer, U. Diskretisierung von Steuerungsproblemen unter stabilen Optimalitätsbedingungen, Habilitationsschrift, Brandenburgische Technische Universitiit Cottbus, 1999. (122 p., in German)
5. Felgenhauer, U. On smoothness properties and approximability of optimal control functions. In D. Klatte, J. Rückmann, and D. Ward, editors, Optimization with Data Perturbation II, vol. 101 of Ann. Oper. Res. Baltzer Sc. Publ., The Netherlands,vol. 101:23-42, 2001.
6. Felgenhauer, U. Structural properties and approximation of optimal controls, Nonlinear Analysis, (TMA), 47(3):1869-1880, 2001.
7. Felgenhauer, U. Weak and strong optimality conditions for constrained control problems with discontinuous control, J. Optim. Theor. Appl., 110(2):361-387, 2001.
8. A. Joffe, S. Reich, and I. Shafrir, editors. Calculus of variations and optimal control. Haifa 1998, vol. 411 of Chapman & Hall/CRC Res. Notes Math., Boca Raton, FL, 2000. Chapman & Hall/CRC.
9. Klotzler, R. On a general conception of duality in optimal control, In: vol. 703 of Lect. Notes Math., 189-196. Springer-Verlag, New York, Heidelberg, Berlin, 1979.
10. Malanowski, K. Two-norm approach in stability and sensitivity analysis of optimization and optimal control problems, Adv. in Math.Sc. and Applic., 2:397-443, 1993.
11. Malanowski, K. Stability and sensitivity analysis of solutions to infinitedimensional optimization problems, In J. Henry nad J.-P. Yvon, editors, Proc. 16th IFIP-TC7 Conference on System Modelling and Optimization, vol. 197 of Lect. Notes in Control and Inf. Sci., 109-127, London, 1994. Springer-Verlag.
12. Malanowski, K. Stability and sensitivity analysis of solutions to nonlinear optimal control problems, Appl. Math. and Optim., 32:111-141, 1995.
13. Malanowski, K. Stability analysis of solutions to parametric optimal control problems, In J. Guddat, H. T. Jongen, F.Noz̧içka, G. Still, and F.Twilt, editors, Proc. IV. Conference on "Parametric Optimization and Related Topics" Enschede 1995, Ser. Approximation and Optimization, 227-244, Frankfurt, 1996. Peter Lang Publ. House.
14. Malanowski, K., Buskens, C., and Maurer, H. Convergence of approximations to nonlinear control problems, In A. V. Fiacco, editor, Mathematical Programming with Data Perturbation, vol. 195 of Lect. Notes Pure Appl. Mathern., 253-284. Marcel Dekker, Inc., New York, 1997.
15. Malanowski, K., and Maurer, H. Sensitivity analysis for parametric optimal control problems with control-state constraints, Comput. Optim. Appl., 5:253-283, 1996.
16. Malanowski, K., and Maurer, H. Sensitivity analysis for state constrained optimal control problems, Discrete Cantin. Dynam. Systems, 4:241-272, 1998.
17. Maurer, H., and Pickenhain, S. Second order sufficient conditions for optimal control problems with mixed control-state constraints, J. Optim. Theor. Appl., 86:649-667, 1995.
18. Milyutin, A. A., and Osmolovskii, N. P. Calculus of variations and optimal control, Amer. Mathern. Soc., Providence, Rhode Island, 1998.
19. Osmolovskii, N. P. Quadratic conditions for nonsingular extremals in optimal control (A theoretical treatment). Russian J. of Mathern. Physics, 2:487-512, 1995.
20. Osmolovskii, N. P. Second-order conditions for broken extremals. In Ioffe et al. [8], pages 198-216.
21. Pickenhain, S. Sufficiency conditions for weak local minima in multidimensional optimal control problems with mixed control-state restrictions, Zeitschr. f. Analysis u. Anwend. (ZAA), 11:559-568, 1992.