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An Introduction to Optimal Control Problems in Life Sciences and Economics : From Mathematical Models to Numerical Simulation with MATLAB® / by Sebastian Aniţa, Viorel Arnăutu, Vincenzo Capasso
Contributor(s): Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: Modeling and Simulation in Science, Engineering and Technology | SpringerLink BücherPublisher: Boston, MA : Springer Science+Business Media, LLC, 2011Description: Online-Ressource (XII, 232p, digital)ISBN:- 9780817680985
- 515.642
- 003.3
- TA342-343
- QA402.3
Contents:
Summary: An Introduction to MATLAB. Elementary Models with Applications -- Optimal Control of Ordinary Differential Systems. Optimality Conditions -- Optimal Control of Ordinary Differential Systems. Gradient Methods -- Optimal Harvesting for Age-Structured Population -- Optimal Control of Diffusive Models -- Appendices -- References -- Index.Summary: Combining two important and growing areas of applied mathematics—control theory and modeling—this textbook introduces and builds on methods for simulating and tackling problems in a variety of applied sciences. Control theory has moved from primarily being used in engineering to an important theoretical component for optimal strategies in other sciences, such as therapies in medicine or policy in economics. Applied to mathematical models, control theory has the power to change the way we view biological and financial systems, taking us a step closer to solving concrete problems that arise out of these systems. Emphasizing "learning by doing," the authors focus on examples and applications to real-world problems, stressing concepts and minimizing technicalities. An elementary presentation of advanced concepts from the mathematical theory of optimal control is provided, giving readers the tools to solve significant and realistic problems. Proofs are also given whenever they may serve as a guide to the introduction of new concepts. This approach not only fosters an understanding of how control theory can open up modeling in areas such as the life sciences, medicine, and economics, but also guides readers from applications to new, independent research. Key features include: * An introduction to the main tools of MATLAB®, as well as programs that move from relatively simple ODE applications to more complex PDE models; * Numerous applications to a wide range of subjects, including HIV and insulin treatments, population dynamics, and stock management; * Exploration of cutting-edge topics in later chapters, such as optimal harvesting and optimal control of diffusive models, designed to stimulate further research and theses projects; * Exercises in each chapter, allowing students a chance to work with MATLAB and achieve a better grasp of the applications; * Minimal prerequisites: undergraduate-level calculus; * Appendices with basic concepts and results from functional analysis and ordinary differential equations, including Runge–Kutta methods; * Supplementary MATLAB files are available at the publisher’s website: http://www.birkhauser-science.com/978-0-8176-8097-8/. As a guided tour to methods in optimal control and related computational methods for ODE and PDE models, An Introduction to Optimal Control Problems in Life Sciences and Economics serves as an excellent textbook for graduate and advanced undergraduate courses in mathematics, physics, engineering, computer science, biology, biotechnology, and economics. The work is also a useful reference for researchers and practitioners working with optimal control theory in these areas.PPN: PPN: 1650944705Package identifier: Produktsigel: ZDB-2-SEB | ZDB-2-SXMS | ZDB-2-SMA
""An Introduction to Optimal Control Problems in Life Sciences and Economics""; ""Preface""; ""Symbols and Notations""; ""Contents""; ""1 An introduction to MATLAB®. Elementary models with applications""; ""1.1 Why MATLAB®?""; ""1.1.1 Arrays and matrix algebra""; ""1.1.2 Simple 2D graphics ""; ""1.1.3 Script files and function files""; ""1.2 Roots and minimum points of 1D functions""; ""1.3 Array-smart functions""; ""1.4 Models with ODEs; MATLAB functions ode23 and ode45""; ""1.5 The spruce budworm model""; ""1.6 Programming Runge--Kutta methods"";""1.7 Systems of ODEs. Models from Life Sciences""""1.8 3D Graphics""; ""Bibliographical Notes and Remarks""; ""Exercises""; ""2 Optimal control of ordinary differential systems. Optimality conditions""; ""2.1 Basic problem. Pontryagin's principle""; ""2.2 Maximizing total consumption""; ""2.3 Maximizing the total population in a predator--prey system""; ""2.4 Insulin treatment model""; ""2.5 Working examples""; ""2.5.1 HIV treatment""; ""2.5.2 The control of a SIR model""; ""Bibliographical Notes and Remarks""; ""Exercises"";""3 Optimal control of ordinary differential systems. Gradient methods""""3.1 A gradient method""; ""3.2 A tutorial example for the gradient method""; ""3.3 Stock management""; ""3.4 An optimal harvesting problem""; ""Bibliographical Notes and Remarks""; ""Exercises""; ""4 Optimal harvesting for age-structured population""; ""4.1 The linear age-structured population dynamics""; ""4.2 The optimal harvesting problem""; ""4.3 A logistic model with periodic vital rates""; ""Bibliographical Notes and Remarks""; ""Exercises""; ""5 Optimal control of diffusive models"";""5.1 Diffusion in mathematical models""""5.2 Optimal harvesting for Fisher's model""; ""5.3 A working example: Control of a reaction--diffusion system""; ""Bibliographical Notes and Remarks""; ""Exercises""; ""A Appendices ""; ""A.1 Elements of functional analysis""; ""A.1.1 The Lebesgue integral""; ""A.1.2 Lp spaces""; ""A.1.3 The weak convergence""; ""A.1.4 The normal cone""; ""A.1.5 The Gâteaux derivative""; ""A.2 Bellman's lemma""; ""A.3 Existence and uniqueness of Carathéodory solution""; ""A.4 Runge--Kutta methods""; ""References""; ""Index""
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