References for short course
OPTIMAL CONTROL THEORY IN APPLICATION TO BIOLOGY
For optimal control of ODES
S. K. Agrawal and B. C. Fabien, Optimization of Dynamics Systems,
Kluwer, 1999.
A. E. Bryson and Y-C Ho, Applied Optimal Control, Hemisphere, 1975.
C. W. Clark, Mathematical Bioeconomics: The Optimal Management of
Renewable Resources, Wiley, 1990.
M. Eisen, Mathematical Methods and Models in the Biological Sciences,
Nonlinear and Multidimensional Theory, Prentice Hall, 1988.
W. H. Fleming and R. W. Rishel, Deterministic and Stochastic Optimal
Control, Springer-Verlag, 1975. (control bible)
R. F. Hartl, S. P. Sethi, and R. G. Vickson, A Survey of the Maximum
Principles for Optimal Control Problems with State Constraints,
SIAM Review 37, 1995, 181-218.
M. I. Kamien, N. L. Schwartz, Dynamic Optimization: The Calculus of Variations
and Optimal Control in Economics and Management, North-Holland, 1991. (readable)
M. Kot, Elements of Mathematical Ecology, Cambridge, 2001.
(one good chapter on control, many good chapters on other stuff)
F. L. Lewis, Optimal Control, Wiley, 1986. (includes discrete case)
J. Macki and A. Strauss, Introduction to Optimal Control Theory,
Springer-Verlang, 1982.
Pontryagin, L. S. , V. G. Boltyanskii, R. V. Gamkrelize, and E. F.
Mishchenko, The Mathematical Theory of Optimal Processes, Wiley, 1962.
S. P. Sethi and G. L. Thompson, Optimal Control Theory: Applications to
Management Science and Economics, Kluwer, 2nd Edition, 2000.
(includes discrete case)
For optimal control of PDEs
X. Li and J. Yong, Optimal Control Theory for Infinite Dimensional Systems,
Birkhauser, 1995.
ODE examples
K.R. Fister, S. Lenhart, and J. S. McNally. Optimizing Chemotherapy in an HIV
Model, Electronic J. Differential Equations 1998 (1998),112.
A. Heinricher, S. Lenhart, and A. Solomon, The Application of Optimal Control
Methodology to a Well-Stirred Bioreactor, Natural Resource Modeling J., 1996,
61-80.
Joshi, H. R., 2002, Optimal Control of an HIV Immunology Model, Optimal
Control Appl. Methods, 23, 199-213.
D. E. Kirschner, S. Lenhart, and S. Serbin, Optimal Control of the Chemotherapy
of HIV, Journal of Math Biology 35(1997), 77-96.
E. Jung, S. Lenhart, and Z. Feng, 2002, Optimal Control of Treatments in a
Two Strain Tuberculosis Model, Discrete and Continuous Dynamical Systems 2,
473-482.
K. R. Fister and J. C. Panetta, Cell-Cycle-Specific Chemotherapy and Optimal
Control, SIAM Journal on Applied Mathematics, Vol. 60, No. 3, pg. 1059-1072.
PDE examples
S. Lenhart and M. Bhat, Application of Distributed Parameter Control Model in
Wildlife Management, Math. Models and Methods in Applied Sciences 4 (1992),
423-439.
M. G. Bhat, K. R. Fister, and S. Lenhart, An Optimal Control Model for Surface
Runoff Contamination of a Large River Basin, Natural Resource Modeling Journal
12 (1999), 175-195.
S. Chawla and S. Lenhart, Application of Optimal Control Theory to in situ
Bioremediation, Computational and Applied Mathematics 114(2000), 81-102.
S. Lenhart, M. Liang, and V. Protopopescu, 1999, Optimal Control of the Effects
of Boundary Habitat Hostility, Math. Methods in the Applied Sciences 22,
1061 - 1077.
K. R. Fister and C. M. McCarthy, Optimal Control of a Chemotaxis System,
Quarterly of Applied Mathematics, Vol LXI, No. 2 193-211, June 2003.
Alternative approaches
J. Hof and M. Bevers, Spatial Optimization for Managed Ecosystems, Columbia
University Press, 1998.
J. Hof and M. Bevers, Spatial Optimization for Ecological Applications,
Columbia University Press, 2002.
L. G. Hanin and L. V. Pavlova, and A. Y. Yakovlev, Biomathematical
Problems in Optimization of Cancer Radiotherapy, CRC Press, 1994.
Suzanne Lenhart and Hem Raj Joshi
University of Tennessee
Mathematics Department
Knoxville, TN 37996-1300 USA
lenhart@math.utk.edu joshi@math.utk.edu
(note Joshi will be working at Xavier University, Cincinnati, this fall)
The following references can be obtained from Renee Fister at renee.fister@murraystate.edu.
1. T. Burden, J. Ernstberger, and K. R. Fister, Optimal Control Applied to Immunotherapy,
Discrete and Continuous Dynamical Systems, Series B, Volume 4, No. 1, pg. 135-146,
to appear February 2004.
2. K. R. Fister and J. C. Panetta, Optimal Control Applied to Cell-Kill Strategies, SIAM
Journal on Applied Mathematics, Volume 63, No. 6, pg. 1954-1971, 2003.
K. Renee Fister
6C Faculty Hall
Department of Mathematics and Statistics
Murray State University
Murray, KY 42071
renee.fister@murraystate.edu