E-Book, Englisch, 274 Seiten
Reihe: Chapman & Hall/CRC Mathematical & Computational Biology
Lenhart / Workman Optimal Control Applied to Biological Models
1. Auflage 2007
ISBN: 978-1-4200-1141-8
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)
E-Book, Englisch, 274 Seiten
Reihe: Chapman & Hall/CRC Mathematical & Computational Biology
ISBN: 978-1-4200-1141-8
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)
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 models.
Focusing on mathematical concepts, the book first examines the most basic problem for continuous time ordinary differential equations (ODEs) before discussing more complicated problems, such as variations of the initial conditions, imposed bounds on the control, multiple states and controls, linear dependence on the control, and free terminal time. In addition, the authors introduce the optimal control of discrete systems and of partial differential equations (PDEs).
Featuring a user-friendly interface, the book contains fourteen interactive sections of various applications, including immunology and epidemic disease models, management decisions in harvesting, and resource allocation models. It also develops the underlying numerical methods of the applications and includes the MATLAB® codes on which the applications are based.
Requiring only basic knowledge of multivariable calculus, simple ODEs, and mathematical models, this text shows how to adjust controls in biological systems in order to achieve proper outcomes.
Zielgruppe
Advanced undergraduate and beginning graduate students as well as professionals in mathematical biology and biomedical engineering.
Autoren/Hrsg.
Fachgebiete
Weitere Infos & Material
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
