Optimal control applied to biological models /
Saved in:
| Author / Creator: | Lenhart, Suzanne. |
|---|---|
| Imprint: | Boca Raton : Chapman & Hall/CRC, c2007. |
| Description: | xii, 261 p. : ill. ; 25 cm. |
| Language: | English |
| Series: | Chapman & Hall/CRC mathematical and computational biology series Chapman and Hall/CRC mathematical & computational biology series. |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/7359362 |
Table of Contents:
- Preface
- 1. Basic Optimal Control Problems
- 1.1. Preliminaries
- 1.2. The Basic Problem and Necessary Conditions
- 1.3. Pontryagin's Maximum Principle
- 1.4. Exercises
- 2. Existence and Other Solution Properties
- 2.1. Existence and Uniqueness Results
- 2.2. Interpretation of the Adjoint
- 2.3. Principle of Optimality
- 2.4. The Hamiltonian and Autonomous Problems
- 2.5. Exercises
- 3. State Conditions at the Final Time
- 3.1. Payoff Terms
- 3.2. States with Fixed Endpoints
- 3.3. Exercises
- 4. Forward-Backward Sweep Method
- 5. Lab 1: Introductory Example
- 6. Lab 2: Mold and Fungicide
- 7. Lab 3: Bacteria
- 8. Bounded Controls
- 8.1. Necessary Conditions
- 8.2. Numerical Solutions
- 8.3. Exercises
- 9. Lab 4: Bounded Case
- 10. Lab 5: Cancer
- 11. Lab 6: Fish Harvesting
- 12. Optimal Control of Several Variables
- 12.1. Necessary Conditions
- 12.2. Linear Quadratic Regulator Problems
- 12.3. Higher Order Differential Equations
- 12.4. Isoperimetric Constraints
- 12.5. Numerical Solutions
- 12.6. Exercises
- 13. Lab 7: Epidemic Model
- 14. Lab 8: HIV Treatment
- 15. Lab 9: Bear Populations
- 16. Lab 10: Glucose Model
- 17. Linear Dependence on the Control
- 17.1. Bang-Bang Controls
- 17.2. Singular Controls
- 17.3. Exercises
- 18. Lab 11: Timber Harvesting
- 19. Lab 12: Bioreactor
- 20. Free Terminal Time Problems
- 20.1. Necessary Conditions
- 20.2. Time Optimal Control
- 20.3. Exercises
- 21. Adapted Forward-Backward Sweep
- 21.1. Secant Method
- 21.2. One State with Fixed Endpoints
- 21.3. Nonlinear Payoff Terms
- 21.4. Free Terminal Time
- 21.5. Multiple Shots
- 21.6. Exercises
- 22. Lab 13: Predator-Prey Model
- 23. Discrete Time Models
- 23.1. Necessary Conditions
- 23.2. Systems Case
- 23.3. Exercises
- 24. Lab 14: Invasive Plant Species
- 25. Partial Differential Equation Models
- 25.1. Existence of an Optimal Control
- 25.2. Sensitivities and Necessary Conditions
- 25.3. Uniqueness of the Optimal Control
- 25.4. Numerical Solutions
- 25.5. Harvesting Example
- 25.6. Beaver Example
- 25.7. Predator-Prey Example
- 25.8. Identification Example
- 25.9. Controlling Boundary Terms
- 25.10. Exercises
- 26. Other Approaches and Extensions
- References
- Index
