Analysis of optimal controls for a mathematical model of tumour anti-angiogenesis

Optimal Control Applications and Methods

Volumn 29, Issue 1, 2008, Pages 41-57

  Ledzewicz, U ^a   Schattier, H ^b  

^a SOUTHERN ILLINOIS UNIVERSITY EDWARDSVILLE   (United States)

^b WASHINGTON UNIVERSITY IN ST LOUIS   (United States)

Author keywords

Bang bang controls; Geometric methods in optimal control; Tumour anti angiogenesis

Indexed keywords

MATHEMATICAL MODELS; ONCOLOGY; PATIENT TREATMENT; TUMORS;

BANG BANG CONTROLS; GEOMETRIC METHODS; OPTIMAL CONTROL PROBLEMS; TUMOUR ANTI ANGIOGENESIS;

OPTIMAL CONTROL SYSTEMS;

EID: 40449120191     PISSN: 01432087     EISSN: 10991514     Source Type: Journal    
DOI: 10.1002/oca.814     Document Type: Article

References (15)

1. Loeb LA. A mutator phenotype in cancer. Cancer Research 2001; 61:3230-3239.
2. Goldie JH. Drug resistance in cancer: a perspective. Cancer and Metastasis Review 2001; 20:63-68.
3. Kerbel RS. A cancer therapy resistant to resistance. Nature 1997; 390:335-336.
4. Hahnfeldt P, Panigrahy D, Folkman J, Hlatky L. Tumor development under angiogenic signaling: a dynamical theory of tumor growth, treatment response, and postvascular dormancy. Cancer Research 1999; 59:4770-4775.
5. d'Onofrio A, Gandolfi A. Tumour eradication by antiangiogenic therapy: analysis and extensions of the model by Hahnfeldt et al. (1999). Mathematical Biosciences 2004; 191:159-184.
6. Ergun A, Camphausen K, Wein LM. Optimal scheduling of radiotherapy and angiogenic inhibitors. Bulletin of Mathematical Biology 2003; 65:407-424.
7. Agur Z, Arakelyan L, Daugulis P, Ginosar Y. Hopf point analysis for angiogenesis models. Discrete and Continuous Dynamical Systems, Series B 2004; 4(1):29-38.
8. Forys U, Keifetz Y, Kogan Y. Critical-point analysis for three-variable cancer angiogenesis models. Mathematical Biosciences and Engineering 2005; 2(3):511-525.
9. Ledzewicz U, Schättier H. Optimal control for a system modelling tumor anti-angiogenesis. ICGST-ACSE Journal 2006; 6:33-39.
10. Ledzewicz U, Schättier H. A synthesis of optimal controls for a model of tumor growth under angiogenic inhibitors. Proceedings of the 44th IEEE Conference on Decision and Control, Sevilla, Spain, December 2005; 934-939.
11. Ledzewicz U, Schättier H. Anti-angiogenic therapy in cancer treatment as an optimal control problem. SIAM Journal on Control and Optimization, accepted.
12. Cesari L. Optimization-Theory and Applications. Springer: New York, 1983.
13. Pontryagin LS, Boltyanskii VG, Gamkrelidze RV, Mishchenko EF. The Mathematical Theory of Optimal Processes. MacMillan: New York, 1964.
14. Bryson AE, Ho YC. Applied Optimal Control. Hemisphere Publishing: Washington, DC, 1975.
15. Krener A. The high-order maximal principle and its application to singular controls. SIAM Journal on Control and Optimization 1977; 15:256-293.