eBook - ePub
Optimal Control in Bioprocesses
Pontryagin's Maximum Principle in Practice
- English
- ePUB (mobile friendly)
- Available on iOS & Android
eBook - ePub
Optimal Control in Bioprocesses
Pontryagin's Maximum Principle in Practice
About this book
Optimal control is a branch of applied mathematics that engineers need in order to optimize the operation of systems and production processes. Its application to concrete examples is often considered to be difficult because it requires a large investment to master its subtleties. The purpose of Optimal Control in Bioprocesses is to provide a pedagogical perspective on the foundations of the theory and to support the reader in its application, first by using academic examples and then by using concrete examples in biotechnology. The book is thus divided into two parts, the first of which outlines the essential definitions and concepts necessary for the understanding of Pontryagin's maximum principle – or PMP – while the second exposes applications specific to the world of bioprocesses. This book is unique in that it focuses on the arguments and geometric interpretations of the trajectories provided by the application of PMP.
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Yes, you can access Optimal Control in Bioprocesses by Jérôme Harmand,Claude Lobry,Alain Rapaport,Tewfik Sari in PDF and/or ePUB format, as well as other popular books in Biological Sciences & Biotechnology. We have over one million books available in our catalogue for you to explore.
Information
PART 1
Learning to use Pontryagin’s Maximum Principle
1
The Classical Calculus of Variations
1.1. Introduction: notations
The theory of optimal control has its roots in the calculus of variations.
The calculus of variations is an ancient branch of mathematics and one of its earliest famous problems was that of Queen Dido. According to legend, in the 9th Century BC, Queen Dido marked the borders of the town of Carthage using the skin of a single bull. She is said to have cut this skin into fine strips to form a very long leather cord with which she formed a semicircle, the two ends of which touched the coast.
Since the 18th Century, using the calculus of variations and the Euler–Lagrange equations, it has been known that if the coast is straight, then the semicircle with a fixed length is indeed the curve that maximizes an integral criterion (the area bordered by the curve and the side that is assumed to be straight, in the Dido problem), with an integral constraint (the length of the curve, in the Dido problem) and whose ends belong to a given set (the coast, assumed to be straight, in the Dido problem) or are fixed.
The term “calculus of variations” refers to a mathematical technique that considers local modifications of a solution curve and that characterizes its (local) optimality if every admissible variation (i.e. such that the disturbed solution passes through the same points A and B and verifies the same integral constraints, if any) has a criterion that is not as good. This is not exactly a “control” problem, but this very technique of “variations” is used to obtain the necessary conditions of opti...
Table of contents
- Cover
- Table of Contents
- Introduction
- PART 1: Learning to use Pontryagin’s Maximum Principle
- PART 2: Applications in Process Engineering
- Appendices
- References
- Index
- End User License Agreement