Optimal Control Applied to Biological Models

BASIC OPTIMAL CONTROL PROBLEMS Preliminaries The Basic Problem and Necessary Conditions Pontryagin's Maximum Principle Exercises EXISTENCE AND OTHER SOLUTION PROPERTIES Existence and Uniqueness Results Interpretation of the Adjoint Principle of Optimality The Hamiltonian and Autonomous Problems Exercises STATE CONDITIONS AT THE FINAL TIME Payoff Terms States with Fixed Endpoints Exercises FORWARD-BACKWARD SWEEP METHOD LAB 1: INTRODUCTORY EXAMPLE LAB 2: MOLD AND FUNGICIDE LAB 3: BACTERIA BOUNDED CONTROLS Necessary Conditions Numerical Solutions Exercises LAB 4: BOUNDED CASE LAB 5: CANCER LAB 6: FISH HARVESTING OPTIMAL CONTROL OF SEVERAL VARIABLES Necessary Conditions Linear Quadratic Regulator Problems Higher Order Differential Equations Isoperimetric Constraints Numerical Solutions Exercises LAB 7: EPIDEMIC MODEL LAB 8: HIV TREATMENT LAB 9: BEAR POPULATIONS LAB 10: GLUCOSE MODEL LINEAR DEPENDENCE ON THE CONTROL Bang-Bang Controls Singular Controls Exercises LAB 11: TIMBER HARVESTING LAB 12: BIOREACTOR FREE TERMINAL TIME PROBLEMS Necessary Conditions Time Optimal Control Exercises ADAPTED FORWARD-BACKWARD SWEEP Secant Method One State with Fixed Endpoints Nonlinear Payoff Terms Free Terminal Time Multiple Shots Exercises LAB 13: PREDATOR-PREY MODEL DISCRETE TIME MODELS Necessary Conditions Systems Case Exercises LAB 14: INVASIVE PLANT SPECIES PARTIAL DIFFERENTIAL EQUATION MODELS Existence of an Optimal Control Sensitivities and Necessary Conditions Uniqueness of the Optimal Control Numerical Solutions Harvesting Example Beaver Example Predator-Prey Example Identification Example Controlling Boundary Terms Exercises OTHER APPROACHES AND EXTENSIONS REFERENCES INDEX