Optimal Control Applied to Biological Models (Chapman & Hall/crc Mathematical Biology Series)

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Optimal Control Applied to Biological Models (Chapman & Hall/crc Mathematical Biology Series)

Lenhart, Suzanne/ Workman, John T.

ウェブストア価格 ¥35,664（本体¥32,422）
Chapman & Hall/CRC（2007/05発売）
外貨定価 US$ 170.00
ポイント 324pt

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製本 Hardcover:ハードカバー版／ページ数 274 p.
言語 ENG
商品コード 9781584886402
DDC分類 570.151

Full Description

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.

Basic Optimal Control Problems. Existence and Other Solution Properties. State Conditions at the Final Time. Forward-Backward Sweep Method. Lab 1: Introductory Example. Lab 2: Mold and Fungicide. Lab 3: Bacteria. Bounded Controls. Lab 4: Bounded Case. Lab 5: Cancer. Lab 6: Fish Harvesting. Optimal Control of Several Variables. Lab 7: Epidemic Model. Lab 8: HIV Treatment. Lab 9: Bear Populations. Lab 10: Glucose Model. Linear Dependence on the Control. Lab 11: Timber Harvesting. Lab 12: Bioreactor. Free Terminal Time Problems. Adapted Forward-Backward Sweep. Lab 13: Predator-Prey Model. Discrete Time Models. Lab 14: Invasive Plant Species. Partial Differential Equation Models. Other Approaches and Extensions. References. Index.