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2011 | Book

An introduction to MATLAB®. Elementary models with applications Read chapter Read first chapter

An Introduction to Optimal Control Problems in Life Sciences and Economics

From Mathematical Models to Numerical Simulation with MATLAB®

Authors: Sebastian Aniţa, Viorel Arnăutu, Vincenzo Capasso

Publisher: Birkhäuser Boston

Book Series : Modeling and Simulation in Science, Engineering and Technology

Part of: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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About this book

Combining two important and growing areas of applied mathematics—control theory and modeling—this textbook introduces and builds on methods for simulating and tackling concrete problems in a variety of applied sciences.

Emphasizing "learning by doing," the authors focus on examples and applications to real-world problems. An elementary presentation of advanced concepts, proofs to introduce new concepts, and carefully presented MATLAB® programs guide the reader through methods in optimal control and related models. This approach not only fosters an understanding of the basic topics, but also leads the way to new, independent research.

With minimal prerequisites and exercises in each chapter, 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, as well as biology, biotechnology, economics, and finance. The work is also a useful reference for researchers and practitioners working with optimal control theory in the above areas.

Table of Contents

Frontmatter
1. An introduction to MATLAB®. Elementary models with applications
Abstract
At the first sight, MATLAB (MATrix LABoratory) is a very flexible and simple programming tool. But it can also be used as high-level programming language. MATLAB is our choice because it offers some important advantages in comparison to other programming languages. This MathWorks TM product contains a general kernel and toolboxes for specialized applications. A beginner should start with the kernel. As already mentioned, the language is easy to learn and to use, but it offers control flow statements, functions, data structures, input/output statements, and other facilities. The Mathematical Function Library provides a large set of functions for a wide range of numerical algorithms. The MATLAB GUI (Graphical User Interface) is also very good and the corresponding functions are easy to use. It is also possible to write C programs that interact with MATLAB code.
Sebastian Aniţa, Viorel Arnăutu, Vincenzo Capasso
2. Optimal control of ordinary differential systems. Optimality conditions
Abstract
This chapter and the next one are devoted to some basic ideas and techniques in optimal control theory of ordinary differential systems. We do not treat the optimal control problem or Pontryagin’s principle in their most general form; instead we prefer a direct approach for some significant optimal control problems in life sciences and economics governed by ordinary differential systems. We point out the main steps in the study of an optimal control problem for each investigated example. These steps are similar for all examples. There are, however, specific technical difficulties for each investigated problem.
Sebastian Aniţa, Viorel Arnăutu, Vincenzo Capasso
3. Optimal control of ordinary differential systems. Gradient methods
Abstract
This chapter is devoted to approximation methods, mainly of gradient type, for optimal control problems governed by ordinary differential equations. The main goal is to build corresponding MATLAB{ $Ⓡ$} programs. The calculation of the gradient of the cost functional allows us to develop gradient-type algorithms. We deal with minimization/maximization problems. As we show, the general principle of a gradient method is the same for both types of problems.
Sebastian Aniţa, Viorel Arnăutu, Vincenzo Capasso
4. Optimal harvesting for age-structured population
Abstract
This chapter is intended to be a bridge towards scientific research on optimal control theory. The problems investigated here are much more complex than those presented in the previous chapters. We focus on optimal harvesting problems for age-structured population dynamics, which are extremely important from a biological as well as from an economical point of view. Even if the degree of complexity of the optimal control problems investigated in this chapter is much higher than before we can see that the steps we have to follow are the same as for the optimal control problems investigated in Chapter 2.
Sebastian Aniţa, Viorel Arnăutu, Vincenzo Capasso
5. Optimal control of diffusive models
Abstract
Mathematical biology has its roots in population ecology, which treats the mathematical modeling of interacting species along the lines established by the mathematicians A. Lotka (1924) and V. Volterra (1926) in terms of nonlinear ordinary differential equations.
Sebastian Aniţa, Viorel Arnăutu, Vincenzo Capasso
Backmatter
Metadata
Title
An Introduction to Optimal Control Problems in Life Sciences and Economics
Authors
Sebastian Aniţa
Viorel Arnăutu
Vincenzo Capasso
Copyright Year
2011
Publisher
Birkhäuser Boston
Electronic ISBN
978-0-8176-8098-5
Print ISBN
978-0-8176-8097-8
DOI
https://doi.org/10.1007/978-0-8176-8098-5

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