Optimal control applied to biological models

✍ Scribed by Lenhart, Suzanne; Workman, John T

• Publisher: Chapman & Hall/CRC
• Year: 2007
• Tongue: English
• Leaves: 272
• Series: Chapman and Hall/CRC mathematical & computational biology series
• Category: Library

✦ Synopsis

"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." "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."--Jacket. 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: 1 Basic Optimal Control Problems 1 --
1.2 The Basic Problem and Necessary Conditions 7 --
1.3 Pontryagin's Maximum Principle 12 --
2 Existence and Other Solution Properties 21 --
2.1 Existence and Uniqueness Results 23 --
2.2 Interpretation of the Adjoint 26 --
2.3 Principle of Optimality 28 --
2.4 The Hamiltonian and Autonomous Problems 31 --
3 State Conditions at the Final Time 37 --
3.1 Payoff Terms 37 --
3.2 States with Fixed Endpoints 41 --
4 Forward-Backward Sweep Method 49 --
5 Lab 1: Introductory Example 57 --
6 Lab 2: Mold and Fungicide 63 --
7 Lab 3: Bacteria 67 --
8 Bounded Controls 71 --
8.1 Necessary Conditions 73 --
8.2 Numerical Solutions 81 --
9 Lab 4: Bounded Case 85 --
10 Lab 5: Cancer 89 --
11 Lab 6: Fish Harvesting 93 --
12 Optimal Control of Several Variables 97 --
12.1 Necessary Conditions 97 --
12.2 Linear Quadratic Regulator Problems 104 --
12.3 Higher Order Differential Equations 107 --
12.4 Isoperimetric Constraints 108 --
12.5 Numerical Solutions 112 --
13 Lab 7: Epidemic Model 117 --
14 Lab 8: HIV Treatment 123 --
15 Lab 9: Bear Populations 129 --
16 Lab 10: Glucose Model 135 --
17 Linear Dependence on the Control 139 --
17.1 Bang-Bang Controls 139 --
17.2 Singular Controls 143 --
18 Lab 11: Timber Harvesting 153 --
19 Lab 12: Bioreactor 157 --
20 Free Terminal Time Problems 163 --
20.1 Necessary Conditions 163 --
20.2 Time Optimal Control 168 --
21 Adapted Forward-Backward Sweep 175 --
21.1 Secant Method 175 --
21.2 One State with Fixed Endpoints 177 --
21.3 Nonlinear Payoff Terms 182 --
21.4 Free Terminal Time 183 --
21.5 Multiple Shots 184 --
22 Lab 13: Predator-Prey Model 189 --
23 Discrete Time Models 193 --
23.1 Necessary Conditions 193 --
23.2 Systems Case 199 --
24 Lab 14: Invasive Plant Species 205 --
25 Partial Differential Equation Models 211 --
25.1 Existence of an Optimal Control 212 --
25.2 Sensitivities and Necessary Conditions 213 --
25.3 Uniqueness of the Optimal Control 215 --
25.4 Numerical Solutions 215 --
25.5 Harvesting Example 216 --
25.6 Beaver Example 220 --
25.7 Predator-Prey Example 223 --
25.8 Identification Example 228 --
25.9 Controlling Boundary Terms 231 --
26 Other Approaches and Extensions 237.

✦ Subjects

Bi