1st Edition
Optimal Control Applied to Biological Models
274 Pages
42 B/W Illustrations
by
Chapman & Hall
274 Pages
by
Chapman & Hall
Also available as eBook on:
From economics and business to the biological sciences to physics and engineering, professionals successfully use the powerful mathematical tool of optimal control to make management and strategy decisions. Optimal Control Applied to Biological Models thoroughly develops the mathematical aspects of optimal control theory and provides insight into the application of this theory to biological... Read more
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
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
Biography
Suzanne Lenhart, John T. Workman
". . . the present book has the merit of collecting and treating in a unitary and accessible manner a large number of relevant problems in mathematical biology; the text is well written, systematically presented, accurate most of the time and accessible to a fairly large audience; it could do a great service to the community of researchers in mathematical control theory . . ."
– Stefan Mirică, in Mathematical Reviews, 2008f
