Optimal control in bioprocesses : Pontryagin's maximum principle in practice / Jérôme Harmand [and three others].

Format:

Book

Author/Creator:

Harmand, Jérôme, author.

Series:

THEi Wiley ebooks.

THEi Wiley ebooks

Language:

English

Subjects (All):

Control theory.

Physical Description:

1 online resource (263 pages)

Edition:

1st ed.

Place of Publication:

London, England ; Hoboken, New Jersey : ISTE : Wiley, 2019.

System Details:

Access using campus network via VPN at home (THEi Users Only).

Summary:

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.

Contents:

Cover

Half-Title Page

Title Page

Copyright Page

Contents

Introduction

PART 1: Learning to use Pontryagin's Maximum Principle

1. The Classical Calculus of Variations

1.1. Introduction: notations

1.2. Minimizing a function

1.2.1. Minimum of a function of one variable

1.2.2. Minimum of a function of two variables

1.3. Minimization of a functional: Euler-Lagrange equations

1.3.1. The problem

1.3.2. The differential of J

1.3.3. Examples

1.4. Hamilton's equations

1.4.1. Hamilton's classical equations

1.4.2. The limitations of classical calculus of variations and small steps toward the control theory

1.5. Historical and bibliographic observations

2. Optimal Control

2.1. The vocabulary of optimal control theory

2.1.1. Controls and responses

2.1.2. Class of regular controls

2.1.3. Reachable states

2.1.4. Controllability

2.1.5. Optimal control

2.1.6. Existence of a minimum

2.1.7. Optimization and reachable states

2.2. Statement of Pontryagin's maximum principle

2.2.1. PMP for the "canonical" problem

2.2.2. PMP for an integral cost

2.2.3. The PMP for the minimum-time problem

2.2.4. PMP in fixed terminal time and integral cost

2.2.5. PMP for a non-punctual target

2.3. PMP without terminal constraint

2.3.1. Statement

2.3.2. Corollary

2.3.3. Dynamic programming and interpretation of the adjoint vector

3. Applications

3.1. Academic examples (to facilitate understanding)

3.1.1. The driver in a hurry

3.1.2. Profile of a road

3.1.3. Controlling the harmonic oscillator: the swing (problem)

3.1.4. The Fuller phenomenon

3.2. Regular problems

3.2.1. A regular Hamiltonian and the associated shooting method

3.2.2. The geodesic problem (seen as a minimum-time problem)

3.2.3. Regularization of the problem of the driver in a hurry.

3.3. Non-regular problems and singular arcs

3.3.1. Optimal fishing problem

3.3.2. Discontinuous value function: the Zermelo navigation problem

3.4. Synthesis of the optimal control, discontinuity of the value function, singular arcs and feedback

3.5. Historical and bibliographic observations

PART 2: Applications in Process Engineering

4. Optimal Filling of a Batch Reactor

4.1. Reducing the problem

4.2. Comparison with Bang-Bang policies

4.3. Optimal synthesis in the case of Monod

4.4. Optimal synthesis in the case of Haldane

4.4.1. Existence of an arc that (partially) separates Θ+ and Θ−

4.4.2. Using PMP

4.5. Historical and bibliographic observations

5. Optimizing Biogas Production

5.1. The problem

5.2. Optimal solution in a well-dimensioned case

5.3. The Hamiltonian system

5.4. Optimal solutions in the underdimensioned case

5.5. Optimal solutions in the overdimensioned case

5.6. Inhibition by the substrate

5.7. Singular arcs

5.8. Historical and bibliographic observations

6. Optimization of a Membrane Bioreactor (MBR)

6.1. Overview of the problem

6.2. The model proposed by Benyahia et al.

6.3. The model proposed by Cogan and Chellamb

6.4. Historical and bibliographic observations

Appendices

Appendix 1: Notations and Terminology

A1.1. Notations

A1.2. Definitions

A1.3. Concepts from topology

Appendix 2: Differential Equations and Vector Fields

A2.1. Existence and uniqueness of solutions

A2.2. Variational equations

A2.3. Solutions for differential equations with time-dependent discontinuities

A2.4. Vector fields

A2.5. Historical and bibliographic observations

Appendix 3: Outline of the PMP Demonstration

A3.1. Principle of demonstration

A3.2. Small elementary variation and the cone Γ.

A3.3. The interior of the cone Γ does not intersect the half-line Π−

A3.4. Introduction of the adjoint vector at time t

A3.5. Historical and bibliographic comments

Appendix 4: Demonstration of PMP without a Terminal Target

A4.1. Demonstration of theorem 2.5

A4.2. Demonstration of the corollary in section 2.1

Appendix 5: Problems that are Linear in the Control

A5.1. Definition of the problem

A5.2. Phase portrait of the Hamilton equations

A5.2.1. Phase portraits of H+ and H−

A5.2.2. Phase portraits of H

A5.3. The relationship with singular arcs

A5.4. The resolution of the optimal control problem

Appendix 6: Calculating Singular Arcs

A6.1. The general case for the dimension n

A6.2. The case of one-dimensional systems

A6.3. The case of two-dimensional systems

References

Index

Other titles from iSTE in Chemical Engineering

EULA.

Notes:

Description based on print version record.

ISBN:

9781119427520

1119427525

9781119597230

1119597234

9781119597377

1119597374

OCLC:

1089524726