Comparison of optimal controls for a model in cancer chemotherapy with L1- and L2-type objectives

Optimization Methods and Software

Volumn 19, Issue 3-4, 2004, Pages 339-350

  Ledzewicz, Urszula ^a   Brown, Tim ^a   Schättler, Heinz ^b  

^a SOUTHERN ILLINOIS UNIVERSITY EDWARDSVILLE   (United States)

^b WASHINGTON UNIVERSITY IN ST LOUIS   (United States)

Author keywords

Cancer chemotherapy; L1 and L2 type objectives; Optimal control; Bilinear systems

Indexed keywords

CELLS; CHEMOTHERAPY; COMPUTER SIMULATION; LINEAR SYSTEMS; MATHEMATICAL MODELS; TUMORS;

BILINEAR SYSTEMS; CANCER CHEMOTHERAPY; L1- AND L2-TYPE OBJECTIVES; OPTIMAL CONTROL;

OPTIMAL CONTROL SYSTEMS;

EID: 3042599337     PISSN: 10556788     EISSN: None     Source Type: Journal    
DOI: 10.1080/10556780410001683104     Document Type: Conference Paper

References (17)

1. M. Eisen (1979). Mathematical Models in Cell Biology and Cancer Chemotherapy, Vol. 30, Lecture Notes in Biomathematics, Springer Verlag.
2. K.R. Fister and J.C. Panetta (2000). Optimal control applied to cell-cycle-specific cancer chemotherapy. SIAM J. Appl. Math., 60, 1059-1072.
3. M. Kimmel and A. Swierniak (1983). An optimal control problem related to leukemia chemotherapy. Sci. Bull. Silesian Tech. Univ., 65, 120-130.
4. D. Kirschner, S. Lenhart and S. Serbin (1997). Optimal control of chemotherapy of HIV. J. Math. Biol., 35, 775-792.
5. U. Ledzewicz and H. Schättler (2002). Optimal bang-bang controls for a 2-compartmem model in cancer chemotherapy. J. Optimiz. Theory Appl. -JOTA, 114, 609-637.
6. U. Ledzewicz and H. Schättler (2002). Analysis of a cell-cycle specifie model for cancer chemotherapy. J. Biol. Syst., 10, 183-206.
7. U. Ledzewicz and H. Schättler (2002). Optimal controls for a 2-compartment model for cancer chemotherapy with quadratic objective. Proceedings of Controls 2002, pp. 241-246, Aveiro, Portugal.
8. R.B. Martin (1992). Optimal control drug scheduling of cancer chemotherapy. Automatica, 28, 1113-1123.
9. J. Noble and H. Schättler (2002). Sufficient conditions for relative minima of broken extremals in optimal control theory. J. Math. Anal. Appl., 269, 98-128.
10. L.S. Pontryagin, V.G. Boltyanskii, R.V. Gamkrelidze and E.F. Mishchenko (1964). The Mathematical Theory of Optimal Processes. MacMillan, New York.
11. J.A.M. Felippe de Souza, M.A.L. Caetano and T. Yoneyama (2000). Optimal control theory applied to the antiviral treatment of AIDS. Proceedings of the 39th IEEE Conference on Decision and Control, pp. 4839-4844, Sydney, Australia.
12. G.W. Swan (1990). Role of optimal control in cancer chemotherapy. Math. Biosci., 101, 237-284.
13. A. Swierniak (1995). Cell cycle as an object of control. J. Biol. Syst., 3, 41-54.
14. A. Swierniak and Z. Duda (1995). Bilinear models of cancer chemotherapy-singularity of optimal solutions. Math. Popul. Dyn., 2, 347-358.
15. A. Swierniak and M. Kimmel (1984). Optimal control application to leukemia chemotherapy protocols design. Sci. Bull. Silesian Tech. Univ., 74, 261-277 (in Polish).
16. A. Swierniak, A. Polanski and Z. Duda (1992). 'Strange' phenomena in simulation of optimal control problems arising in cancer chemotherapy. Proceedings of the 8th Prague Symposium on Computer Simulation in Biology, Ecology and Medicine, pp. 58-62.
17. A. Swierniak, A. Polanski and M. Kimmel (1996). Optimal control problems arising in cell-cycle-specific cancer chemotherapy. Cell Prolif., 29, 117-139.