Optimal control applied to biological models

Detalles Bibliográficos
Autor principal: Lenhart, Suzanne
Otros Autores: Workman, John T.
Formato: Libro
Lenguaje:English
Publicado: Boca Raton : Chapman & Hall/CRC, ©2007.
Colección:Chapman and Hall/CRC mathematical & computational biology series.
Materias:
Modelos biológicos
Optimización matemática
Acceso en línea:http://catdir.loc.gov/catdir/toc/ecip078/2007000973.html
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Tabla de Contenidos:
  • 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.

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