Optimal Control Applied to Biological Models (Hardcover)

BASIC OPTIMAL CONTROL PROBLEMS Preliminaries The Basic Problem and Necessary Conditions Pontryagin's Maximum Principle ExercisesEXISTENCE AND OTHER SOLUTION PROPERTIES Existence and Uniqueness Results Interpretation of the Adjoint Principle of Optimality The Hamiltonian and Autonomous Problems ExercisesSTATE CONDITIONS AT THE FINAL TIME Payoff TermsStates with Fixed EndpointsExercisesFORWARD-BACKWARD SWEEP METHOD LAB 1: INTRODUCTORY EXAMPLE LAB 2: MOLD AND FUNGICIDELAB 3: BACTERIABOUNDED CONTROLS Necessary Conditions Numerical Solutions ExercisesLAB 4: BOUNDED CASE LAB 5: CANCER LAB 6: FISH HARVESTINGOPTIMAL CONTROL OF SEVERAL VARIABLES Necessary Conditions Linear Quadratic Regulator Problems Higher Order Differential EquationsIsoperimetric Constraints Numerical Solutions Exercises LAB 7: EPIDEMIC MODEL LAB 8: HIV TREATMENT LAB 9: BEAR POPULATIONS LAB 10: GLUCOSE MODELLINEAR DEPENDENCE ON THE CONTROL Bang-Bang ControlsSingular Controls Exercises LAB 11: TIMBER HARVESTINGLAB 12: BIOREACTOR FREE TERMINAL TIME PROBLEMS Necessary Conditions Time Optimal Control ExercisesADAPTED FORWARD-BACKWARD SWEEP Secant Method One State with Fixed EndpointsNonlinear 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 SPECIESPARTIAL DIFFERENTIAL EQUATION MODELS Existence of an Optimal ControlSensitivities 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 REFERENCESINDEX