Optimality properties of controls with bang-bang components in problems with semilinear state equation

Control and Cybernetics

Volumn 34, Issue 3, 2005, Pages 763-785

  Felgenhauer, Ursula ^a  

^a BRANDENBURG UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

Bang bang control; Optimality conditions; Riccati equation; Sensitivity; Switching points optimization

Indexed keywords

EID: 31544438296     PISSN: 03248569     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Conference Paper

References (16)

1. AGRACHEV, A., STEFANI, G. and ZEZZA, P.L. (2002) Strong optimality for a bang-bang trajectory. SIAM J. Control Optim. 41, 991-1014.
2. FELGENHAUER, U. (2001a) Weak and strong optimality in a problem with discontinuous control behavior. J. Optim. Theor. Appl. 110, 361-387.
3. FELGENHAUER, U. (2001b) Stability and local growth near bounded-strong local optimal controls. In: E. Sachs and R. Tichatschke, eds., System Modelling and Optimization XX, 20th IFIP TC7 Conference Trier 2001; Kluwer Academic Publ., Dordrecht, The Netherlands, 2003, 213-227.
4. FELGENHAUER, U. (2003a) On stability of bang-bang type controls. SIAM J. Control Optim. 41 (6), 1843-1867.
5. FELGENHAUER, U. (2003b) Optimality and sensitivity properties of bang-bang controls for linear systems. In: J. Cagnol, J.-P. Zolesio, eds., Information Processing: Recent Mathematical Advances in Optimization and Control, 21st IFIP TC7 Conference Sophia Antipolis 2003; Presses de l'Ecole des Mines de Paris, 2004, 87-99.
6. FELGENHAUER, U. (2004) Optimality and sensitivity for semilinear bang-bang type optimal control problems. Internat. J. Appl. Math. Computer Sc. 14 (4), 447-454.
7. KIM, J.R. and MAURER, H. (2003) Sensitivity analysis of optimal control problems with bang-bang controls. In: Proc. IEEE-Conference on Decision and Control, Hawaii 2003, 4, 3281-3286.
8. KLÖTZLER, R. (1979) On a general conception of duality in optimal control. Lect. Notes Math. 703, 189-196, Springer, New York.
9. MALANOWSKI, K. (2001) Stability and sensitivity analysis for optimal control problems with control-state constraints. Dissertationes Mathematicae, Polska Akad. Nauk, Inst. Matemat., Warszawa.
10. MAURER, H. and OSMOLOVSKII, N.P. (2004) Second order sufficient conditions for time-optimal bang-bang control. SIAM J. Control Optim. 42 (6), 2239-2263.
11. MAURER, H. and PICKENHAIN, S. (1995) Second order sufficient conditions for optimal control problems with mixed control-state constraints. J. Optim. Theor. Appl. 86, 649-667.
12. MILYUTIN, A.A. and OSMOLOVSKII, N.P. (1998) Calculus of Variations and Optimal Control. Amer. Mathem. Soc., Providence, Rhode Island.
13. NOBLE, J. and SCHAETTLER, H. (2002) Sufficient conditions for relative minima of broken extremals in optimal control theory. J. Math. Anal. Appl. 269, 98-128.
14. OSMOLOVSKII, N.P. (2000) Second-order conditions for broken extremals. In: A. Ioffe et al., eds., Calculus of Variations and Optimal Control, Chapman & Hall/CRC Res. Notes Math. 411, Boca Raton, FL, 198-216.
15. OSMOLOVSKII N.P. and LEMPIO, F. (2002) Transformation of quadratic forms to perfect squares for broken extremals. Set-Valued Analysis 10, 209-232.
16. SARYCHEV, A.V. (1997) First- and second-order sufficient optimality conditions for bang-bang controls. SIAM J. Control Optim. 35, 315-340.