Abstract
We consider a computational approach to solving an optimal control formulation of optimal drug scheduling in HIV infected individuals. The optimal control problem is transformed using the control parameterisation enhancing technique (CPET), which enables efficient computation of an optimal control using a relatively coarse discretisation. A number of numerical difficulties with the model are discussed, and for illustration, numerical examples are solved.
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References
Fister, K.R., S. Lenhart, and J.S. McNally. (1998). “Optimizing Chemotherapy in an HIV Model.” Electronic Journal of Differential Equations 1998(32), 1–12.
Hraba, T. and J. Doležal. (1994). “Mathematical Modelling Approach to AIDS Pathogenesis and Treatment.” In Proceedings of the IFIP, Prague, Czech Republic.
Hraba, T. and J. Doležal. (1996). “A Mathematical Model and CD4+ Lymphocyte Dynamics in HIV Infection.” Emerging Infectious Diseases 2(4), 299–305.
Lee, H.W.J., X.Q. Cai, and K.L. Teo. (2001). “An Optimal Control Approach to Manpower Planning Problem.” In Mathematical Problems in Engineering, pp. 155–175.
Lee, H.W.J., K.L. Teo, and X.Q. Cai. (1998). “An Optimal Control Approach to Nonlinear Mixed Integer Programming Problems.” Computers and Mathematics with Applications 36(3), 87–105.
Lee, H.W.J., K.L. Teo, and E.B. Lim. (2001). “Sensor Scheduling in Continuous Time.” Automatica 37, 2017–2023.
Lee, H.W.J., K.L. Teo, L.S. Jennings, and V. Rehbock. (1997). “Control Parametrization Enhancing Technique for Time Optimal Control Problems.” Dynamic Systems and Applications 6, 243–262.
Lee, H.W.J., K.L. Teo, L.S. Jennings, and V. Rehbock. (1999). “Control Parametrization Enhancing Technique for Optimal Discrete-Valued Problems.” Automatica 35(8).
Lee, H.W.J., W.R. Lee, S. Wang, and K.L. Teo. (2001). “Construction of Global Sub-Optimal Feedback Control for Chaotic Systems Using B-Spline with Optimally Chosen Knot Points.” International Journal of Bifurcation and Chaos in Applied Science and Engineering 11(9).
Myburgh, C.D. and K.H. Wong. (2001). “An Optimal Control Approach to Therapeutic Intervention in HIV Infected Individuals.” In Proceedings of the Third International Conference on Control Theory and Applications, Pretoria, South Africa.
Teo, K.L., L.S. Jennings, H. Lee, and V. Rehbock. (2005). “The Control Parametrization Enhancing Transform for Constrained Optimal Control Problems.” Journal of the Australian Mathematics Society, Series B.
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Myburgh, C., Wong, K.H. Computational Control of an HIV Model. Ann Oper Res 133, 277–283 (2005). https://doi.org/10.1007/s10479-004-5038-6
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DOI: https://doi.org/10.1007/s10479-004-5038-6