Bezier Control Points Method to Solve Scheduling of Injections of Immunotherapeutic Agents

Show more

References

[1] A. Cappuccio, F. Castiglione and B. Piccoli, “Determination of the Optimal Therapeutic Protocols in Cancer Immunotherapy,” Mathematical Biosciences, Vol. 209, No. 1, 2007, pp. 1-13. doi:10.1016/j.mbs.2007.02.009

[2] B. Piccoli and F. Castiglione, “Optimal Vaccine Scheduling in Cancer Immunotherapy,” Physica A, Vol. 370, No. 2, 2006, pp. 672-680.
doi:10.1016/j.physa.2006.03.011

[3] C. P. Neuman and A. Sen, “A Suboptimal Control Algoithm for Constrained Problems Using Cubic Splines,” Automatica, Vol. 9, No. 5, 1973, pp. 601-613.
doi:10.1016/0005-1098(73)90045-9

[4] G. Elnagar, M. Kazemi and M. Razzaghi, “The Pseudospectral Legendre Method for Discretizing Optimal Control Problem,” IEEE Transactions on Automatic Control, Vol. 40, No. 10, 1965, pp. 1793-1796.
doi:10.1109/9.467672

[5] H. Jaddu, “Spectral Method for Constrained Linearquadratic Optimal Control,” Mathematicas and Computers in Simulation, Vol. 58, No. 2, 2002, pp. 159-169.
doi:10.1016/S0378-4754(01)00359-7

[6] H. R. Sirisena, “Computation of Optimal Controls Using a Piecewise Polynomial Parameterization,” IEEE Transactions on Automatic Control, Vol. 18, No. 4, 1973, pp. 409-411. doi:10.1109/TAC.1973.1100329

[7] H. R. Sirisena and F. S. Chou, “State Parameterization Approach to the Solution of Optimal Control Problems,” Optimal Control Applications and Methods, Vol. 2, No. 3, 1981, pp. 289-298. doi:10.1002/oca.4660020307

[8] I. Troch, F. Breitenecker and M. Graeff, “Computing Optimal Controls for Systems with State and Control Constraints,” Proceedings of the IFAC Control Applications of Nonlinear Programming and Optimization, Paris, 7-9 June 1989, pp. 39-44.

[9] J. Vlassenbroeck, “A Chebyshev Polynomial Method for Optimal Control with State Constraints,” Automatica, Vol. 24, No. 4, 1988, pp. 499-504.
doi:10.1016/0005-1098(88)90094-5

[10] K. Teo, C. Goh and K. Wong, “A Unified Computational Approach to Optimal Control Problem,” Longman, Harlow, 1981.

[11] M. Evrenosoglu and S. Somali, “Least Squares Methods for Solving Singularity Perturbed Two-Points Boundary Value Problems Using Bezier Control Point,” Applied Mathematics Letters, Vol. 21, No. 10, 2008, pp. 10291032. doi:10.1016/j.aml.2007.10.021

[12] P. A. Frick and D. J. Stech, “Solution of Optimal Control Problems on a Parallel Machine Using the Epsilon Method,” Optimal Control Applications and Methods, Vol. 16, 1995, pp. 1-17.

[13] R. Pytlak, “Numerical Methods for Optimal Control Problems with State Constraints,” Springer-Veriag, Berlin, 1999.

[14] V. Yen and M. Nagurka, “Optimal Control of Linearly Constrained Linear Systems via State Parameterization,” Optimal Control Applications and Methods, Vol. 13, No. 2, 1992, pp. 155-167. doi:002/oca.4660130206

[15] V. Kuznetsov, I. Makalkin, M. Taylor and A. Perelson, “Nonlinear Dynamics of Immunogenic Tumors Parameter Estimation and Global Bifurcation Analysis,” Bulletin of Mathematical Biology, Vol. 56, No. 2, 1994, pp. 295-321.

[16] D. Kirschner and J. C. Panetta, “Modeling Immunotherapy of Tumor-Immune Interaction,” Journal of Mathematical Biology, Vol. 37, No. 3, 1998, pp. 235-252.
doi:10.1007/s002850050127

[17] T. Burden, J. Ernstberger and K. R. Fister, “Optimal Control Applied to Immunotherapy,” Discrete and Continuous Dynamical Systems Series B, Vol. 4, No. 1, 2004, pp. 135-146.

[18] A. Ghaffari and N. Naserufar, “Optimal Therapeutic Protocols in Cancer Immunotherapy,” Computers in Biology and Medicine, Vol. 40, No. 3, 2010, pp. 261-270.
doi:10.1016/j.compbiomed.2009.12.001