An Introduction to Optimal Control Problems in Life Sciences and Economics: From Mathematical Models to Numerical Simulation with MATLAB®

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Springer Science & Business Media, May 5, 2011 - Mathematics - 232 pages
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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.

 

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Contents

1 An introduction to MATLAB Elementary models with applications
1
2 Optimal control of ordinary differential systems Optimality conditions
59
3 Optimal control of ordinary differential systems Gradient methods
99
4 Optimal harvesting for agestructured population
144
5 Optimal control of diffusive models
185
A Appendices
207
References
227
Index
232
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About the author (2011)

Sebastian Aniţa is Full Professor on the Faculty of Mathematics at the University “Al.I. Cuza” Iaşi, Romania. His research interests include: optimal control of partial differential equations; mathematical biology; mathematical models in the applied sciences; and industrial problems in the areas of heat transfer and materials science. Professor Aniţa is the author of more than 50 scientific papers in refereed international journals, one monograph, and three textbooks.

Viorel Arnaŭtu is Full Professor on the Faculty of Mathematics at the University “Al.I. Cuza” Iaşi, Romania. His research interests include: numerical methods (theory, algorithms and computer programs) for optimal control problems; numerical methods for Hamilton-Jacobi equations; numerical methods for PDEs and integral equations; and applications to free boundary problems, epidemic models, optimization of plates, laser hardening of steel, 3-D curved mechanical structures, and population dynamics. Professor Arnaŭtu is the author of more than 30 scientific papers in refereed international journals, one monograph, and one textbook.

Vincenzo Capasso is Professor of Probability and Mathematical Statistics at the University of Milano, Italy. He is the Founder and Director of MIRIAM (Milan Research Centre for Industrial and Applied Mathematics) and later of ADAMSS (Research Centre for Advanced Applied Mathematical and Statistical Sciences) at the University of Milan. His research interests include: spatially structured stochastic processes; stochastic geometry; reaction-diffusion systems; statistics of structured stochastic processes; and applications to biology, medicine, and industrial problems. Professor Capasso is the author of more than 150 scientific papers and approximately 10 monographs, edited books, and textbooks by international scientific publishing companies.