Optimal Control Applied to Biological Models

✍ Scribed by Lenhart, Suzanne; Workman, John T

• Publisher: CRC Press
• Year: 2007
• Tongue: English
• Leaves: 272
• Series: Chapman & Hall/CRC Mathematical and Computational Biology
• Category: Library

✦ Synopsis

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 HA. Read more...

Abstract:

Develops the mathematical aspects of optimal control theory and provides insight into the application of this theory to biological models. This book examines the basic problem for continuous time ordinary differential equations (ODEs). It introduces the optimal control of discrete systems and of partial differential equations (PDEs). Read more...

✦ Table of Contents

Content: Front cover
Published Titles
Contents
Preface
Chapter 1: Basic Optimal Control Problems
Chapter 2: Existence and Other Solution Properties
Chapter 3: State Conditions at the Final Time
Chapter 4: Forward-Backward Sweep Method
Chapter 5: Lab 1: Introductory Example
Chapter 6: Lab 2: Mold and Fungicide
Chapter 7: Lab 3: Bacteria
Chapter 8: Bounded Controls
Chapter 9: Lab 4: Bounded Case
Chapter 10: Lab 5: Cancer
Chapter 11: Lab 6: Fish Harvesting
Chapter 12: Optimal Control of Several Variables
Chapter 13: Lab 7: Epidemic Model
Chapter 14: Lab 8: HIV Treatment Chapter 15: Lab 9: Bear PopulationsChapter 16: Lab 10: Glucose Model
Chapter 17: Linear Dependence on the Control
Chapter 18: Lab 11: Timber Harvesting
Chapter 19: Lab 12: Bioreactor
Chapter 20: Free Terminal Time Problems
Chapter 21: Adapted Forward-Backward Sweep
Chapter 22: Lab 13: Predator-Prey Model
Chapter 23: Discrete Time Models
Chapter 24: Lab 14: Invasive Plant Species
Chapter 25: Partial Di®erential Equation Models
Chapter 26: Other Approaches and Extensions
References
Back cover