Optimal control for chemical engineers:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton ; London ; New York
CRC Press, Taylor & Francis Group
[2013]
|
| Schlagworte: | |
| Online-Zugang: | kostenfrei kostenfrei Inhaltsverzeichnis Klappentext |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | xvii, 290 Seiten Diagramme |
| ISBN: | 9781439838945 |
Internformat
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| 264 | 4 | |c © 2013 | |
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| 650 | 4 | |a Chemical process control | |
| 650 | 4 | |a Mathematical optimization | |
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Datensatz im Suchindex
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| adam_text |
Contents
Preface
xiii
Notation xv
1
Introduction
1
1.1 Definition. 1
1.2 Optimal
Control
versus
Optimization .
4
1.3
Examples of
Optimal
Control
Problems. 5
1.3.1
Batch Distillation
. 5
1.3.2
Plug Flow Reactor
. 6
1.3.3
Heat Exchanger
. 8
1.3.4
Gas Diffusion in
a Non-
Volatile Liquid
. 9
1.3.5
Periodic Reactor
. 11
1.3.6
Nuclear Reactor
. 12
1.3.7
Vapor Extraction of Heavy Oil
. 13
1.3.8
Chemotherapy
. 15
1.3.9
Medicinal Drug Delivery
. 16
1.3.10
Blood Flow and Metabolism
. 17
1.4
Structure of Optimal Control Problems
. 19
Bibliography
. 20
Exercises
. 21
2 Fundamental
Concepts
23
2.1
From Function to Functional
. 23
2.1.1
Functional as a Multivariable Function
. 25
2.2
Domain of a Functional
. 25
2.2.1
Linear or Vector Spaces
. 26
2.2.2
Norm of a Function
. 26
2.3
Properties of Functionals
. 27
2.4
Differential of a Functional
. 28
2.4.1
Frédiét
Differential
. 28
2.4.2
Gâteaux
Differential
. 30
2.4.3
Variation
. 36
2.4.4
Summary of Differentials
. 38
2.4.5
Relations between Differentials
. 38
2.5
Variation of an Integral Objective Functional
. 40
2.5.1
Equivalence to Other Differentials
. 41
VII
vin
2.5.2
Application to
Optimal
Control Problems
. 44
2.6
Second Variation
. 50
2.6.1
Second Degree Homogeneity
. 50
2.6.2
Contribution to Functional Change
. 51
2.
A Second-Order Taylor Expansion
. 52
Bibliography
. 54
Exercises
. 54
Optimality in Optimal Control Problems
57
3.1
Necessary Condition for Optimality
. 57
3.2
Application to Simplest Optimal Control Problem
. 58
3.2.1
Augmented Functional
. 59
3.2.2
Optimal Control Analysis
. 59
3.2.3
Generalization
. 67
3.3
Solving an Optimal Control Problem
. 71
3.3.1
Presence of Several Local Optima
. 73
3.4
Sufficient Conditions
. 74
3.4.1
Weak Sufficient Condition
. 75
3.5
Piecewise Continuous Controls
. 76
3.A Differentiability of
λ
. 78
3.B Vanishing of (Fy
4-
\Gy
+
λ)
at
ŕ
= 0 . 81
3.C Mangasarian Sufficiency Condition
. 81
Bibliography
. 83
Exercises
. 84
Lagrange
Multipliers
87
4.1
Motivation
. 87
4.2
Role of
Lagrange
Multipliers
. 88
4.3 Lagrange
Multiplier Theorem
. 88
4.3.1
Generalization to Several Equality Constraints
. 94
4.3.2
Generalization to Several Functions
. 96
4.3.3
Application to Optimal Control Problems
. 99
4.4 Lagrange
Multiplier and Objective Functional
. 107
4.4.1
General Relation
. 109
4.5
John Multiplier Theorem for Inequality Constraints
. 109
4.5.1
Generalized John Multiplier Theorem
. 113
4.5.2
Remark on Numerical Solutions
. 115
4.
A Inverse Function Theorem
. 115
Bibliography
. 120
Exercises
. 121
їх
Pontryagin's
Minimum
Principle
123
5.1
Application
. 123
5.2
Problem
Statement .
126
5.2.1
Class of
Controls
. 126
5.2.2
New State Variable
. 127
5.2.3
Notation
. 127
5.3
Pontryagin's Minimum Principle
. 128
5.3.1
Assumptions
. 128
5.3.2
Statement
. 129
5.4
Derivation of Pontryagin's Minimum Principle
. 129
5.4.1
Pulse Perturbation of Optimal Control
. 131
5.4.2
Temporal Perturbation of Optimal Control
. 134
5.4.3
Effect on Final State
. 134
5.4.4
Choice of Final
Costate
. 136
5.4.5
Minimality of the Hamiltonian
. 137
5.4.6
Zero Hamiltonian at Free Final Time
. 145
5.
A Convexity of Final States
. 145
5.
В
Supporting
Hyperplane
of a Convex Set
. 149
Bibliography
. 152
Different Types of Optimal Control Problems
153
6.1
Free Final Time
. 153
6.1.1
Free Final State
. 153
6.1.2
Fixed Final State
. 157
6.1.3
Final State on Hypersurfaces
. 158
6.2
Fixed Final Time
. 161
6.2.1
Free Final State
. 161
6.2.2
Fixed Final State
. 161
6.2.3
Final State on Hypersurfaces
. 162
6.3
Algebraic Constraints
. 163
6.3.1
Algebraic Equality Constraints
. 163
6.3.2
Algebraic Inequality Constraints
. 166
6.4
Integral Constraints
. 168
6.4.1
Integral Equality Constraints
. 168
6.4.2
Integral Inequality Constraints
. 171
6.5
Interior Point Constraints
. 172
6.6
Discontinuous Controls
. 177
6.7
Multiple Integral Problems
. 178
Bibliography
. 182
Exercises
. 183
Numerical Solution of Optimal Control Problems
185
7.1
Gradient Method
. 185
7.1.1
Free Final Time and Free Final State
. 185
7.1.2
Iterative Procedure
. 186
7.1.3
Improvement Strategy
. 187
7.1.4
Algorithm for the Gradient Method
. 191
7.1.5
Fixed Final Time and Free Final State
. 199
7.2
Penalty Function Method
. 201
7.2.1
Free Final Time and Final State on Hypersurfaces
. . 201
7.2.2
Free Final Time but Fixed Final State
. 207
7.2.3
Algebraic Equality Constraints
. 209
7.2.4
Integral Equality Constraints
. 214
7.2.5
Algebraic Inequality Constraints
. 217
7.2.6
Integral Inequality Constraints
. 221
7.3
Shooting Newton-Raphson Method
. 223
7.
A Derivation of Steepest Descent Direction
. 229
7.
A.I Objective
. 229
7.A.2 Sufficiency Check
. 230
Bibliography
. 231
Exercises
. 231
Optimal Periodic Control
235
8.1
Optimality of Periodic Controls
. 235
8.1.1
Necessary Conditions
. 236
8.2
Solution Methods
. 239
8.2.1
Successive Substitution Method
. 239
8.2.2
Shooting Newton-Raphson Method
. 239
8.3
Pi Criterion
. 248
8.4
Pi Criterion with Control Constraints
. 256
8.
A Necessary Conditions for Optimal Steady State
. 260
8.B Derivation of Equation
(8.12). 261
8.C Fourier Transform
. 264
8.
D
Derivation of Equation
(8.25). 265
Bibliography
. 265
Exercises
. 266
Mathematical Review
267
9.1
Limit of a Function
. 267
9-2
Continuity of a Function
. 267
9.2.1
Lower and Upper Semi-Continuity
. 268
9.3
Intervals and Neighborhoods
. 268
9.4
Bounds
. 269
9.5
Order of Magnitude
. 269
9.5.1
Big-0 Notation
. 269
9.6
Taylor Series and Remainder
. 270
Xl
9.7
Autonomous Differential Equations
. 270
9.7.1
Non-Autonomous to Autonomous Transformation
. . 270
9.8
Differential
. 271
9.9
Derivative
. 272
9.9.1
Directional Derivative
. 272
9.10
Leibniz Integral Rule
. 273
9.11
Xewton-Raphson Method
. 273
9.12
Composite Simpson's
1/3
Rule
. 275
9.13
Fundamental Theorem of Calculus
. 275
9.14
Mean Value Theorem
. 276
9.14.1
For Derivatives
. 276
9.14.2
For Integrals
. 276
9.15
Intermediate Value Theorem
. 276
9.16
Implicit Function Theorem
. 277
9.17
Bolzano-Weierstrass Theorem
. 277
9.18
Weierstrass
Theorem
. 278
9.19
Linear or Vector Space
. 278
9.20
Direction of a Vector
. 279
9.21
Parallelogram Identity
. 280
9.22
Triangle Inequality for Integrals
. 280
9.23
Cauchy-Schwarz Inequality
. 281
9.24
Operator Inequality
. 281
9.25
Conditional Statement
. 282
9.26
Fundamental Matrix
. 283
Bibliography
. 283
Index
285
CHEMICAL ENGINEERING
Optimal Control for
Chemical Engineers
Optimal Control for Chemical Engineers gives a detailed treatment of
optimal control theory that enables you to formulate and solve optimal
control problems. With a strong emphasis on problem solving, the book
provides all the necessary mathematical analyses and derivations of
important results.
The text begins by introducing various examples and basic concepts of
optimal control. It then analyzes the notion of optimality, describes the
ubiquitous
Lagrange
multipliers, and presents the celebrated Pontryagin
principle of optimal control. Building on this foundation, the author
examines different types of optimal control problems as well as the required
conditions for optimality. He also describes important numerical methods
and computational algorithms for solving a wide range of optimal
control problems.
Features
*
Presents the necessary mathematical background using
numerous examples
*
Includes key mathematical results along with their derivations
*
Focuses on problem formulation and solving
*
Incorporates detailed computational algorithms and solutions
of several example problems
*
Devotes a whole chapter to periodic optimal control
Through its lucid development of optimal control theory and computational
algorithms, this self-contained book shows you how to solve a variety of
optimal control problems.
CRC
Press
6000
Broken Sound Parkway. NW
Suite
300,
Boca Raton, FL
33487
711
Third
Акепие
New Yorx, NY
10017
2
Park Square, Milton
РапЧ
Abingdon
Ошл
ΟΧΙ
4
4RN, UK
9ł781439T838945'
www.crcpress.com |
| any_adam_object | 1 |
| author | Upreti, Simant Ranjan |
| author_GND | (DE-588)1139209906 |
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| author_role | aut |
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| author_variant | s r u sr sru |
| building | Verbundindex |
| bvnumber | BV040605982 |
| callnumber-first | T - Technology |
| callnumber-label | TP155 |
| callnumber-raw | TP155.75 |
| callnumber-search | TP155.75 |
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| callnumber-subject | TP - Chemical Technology |
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| dewey-full | 519.6 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.6 |
| dewey-search | 519.6 |
| dewey-sort | 3519.6 |
| dewey-tens | 510 - Mathematics |
| discipline | Chemie / Pharmazie Chemie-Ingenieurwesen Mathematik |
| format | Book |
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| id | DE-604.BV040605982 |
| illustrated | Not Illustrated |
| indexdate | 2025-01-22T21:01:38Z |
| institution | BVB |
| isbn | 9781439838945 |
| language | English |
| lccn | 2012030747 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025433651 |
| oclc_num | 844023412 |
| open_access_boolean | 1 |
| owner | DE-12 DE-634 DE-210 DE-521 DE-1102 DE-1046 DE-1028 DE-1050 DE-573 DE-M347 DE-92 DE-1051 DE-898 DE-BY-UBR DE-859 DE-860 DE-1049 DE-861 DE-863 DE-BY-FWS DE-862 DE-BY-FWS DE-Re13 DE-BY-UBR DE-Y3 DE-255 DE-Y7 DE-Y2 DE-70 DE-2174 DE-127 DE-22 DE-BY-UBG DE-155 DE-BY-UBR DE-91 DE-BY-TUM DE-91G DE-BY-TUM DE-384 DE-473 DE-BY-UBG DE-19 DE-BY-UBM DE-355 DE-BY-UBR DE-703 DE-20 DE-706 DE-824 DE-29 DE-739 |
| owner_facet | DE-12 DE-634 DE-210 DE-521 DE-1102 DE-1046 DE-1028 DE-1050 DE-573 DE-M347 DE-92 DE-1051 DE-898 DE-BY-UBR DE-859 DE-860 DE-1049 DE-861 DE-863 DE-BY-FWS DE-862 DE-BY-FWS DE-Re13 DE-BY-UBR DE-Y3 DE-255 DE-Y7 DE-Y2 DE-70 DE-2174 DE-127 DE-22 DE-BY-UBG DE-155 DE-BY-UBR DE-91 DE-BY-TUM DE-91G DE-BY-TUM DE-384 DE-473 DE-BY-UBG DE-19 DE-BY-UBM DE-355 DE-BY-UBR DE-703 DE-20 DE-706 DE-824 DE-29 DE-739 |
| physical | xvii, 290 Seiten Diagramme |
| psigel | ZDB-7-TOA ZDB-94-OAB |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | CRC Press, Taylor & Francis Group |
| record_format | marc |
| spelling | Upreti, Simant Ranjan Verfasser (DE-588)1139209906 aut Optimal control for chemical engineers Simant Ranjan Upreti Boca Raton ; London ; New York CRC Press, Taylor & Francis Group [2013] © 2013 xvii, 290 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Chemie Chemical process control Mathematical optimization SCIENCE / Chemistry / Industrial & Technical bisacsh TECHNOLOGY & ENGINEERING / Electrical bisacsh Optimierung (DE-588)4043664-0 gnd rswk-swf Chemische Verfahrenstechnik (DE-588)4069941-9 gnd rswk-swf Technische Chemie (DE-588)4078178-1 gnd rswk-swf Prozessoptimierung (DE-588)4176074-8 gnd rswk-swf Prozessüberwachung (DE-588)4133922-8 gnd rswk-swf Prozessüberwachung (DE-588)4133922-8 s DE-604 Prozessoptimierung (DE-588)4176074-8 s Technische Chemie (DE-588)4078178-1 s Chemische Verfahrenstechnik (DE-588)4069941-9 s Optimierung (DE-588)4043664-0 s Erscheint auch als Online-Ausgabe https://www.doabooks.org/doab?func=fulltext&uiLanguage=en&rid=48330 Verlag kostenfrei Volltext https://www.doabooks.org/doab?func=fulltext&uiLanguage=en&rid=48420 Verlag kostenfrei Volltext Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025433651&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025433651&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Upreti, Simant Ranjan Optimal control for chemical engineers Chemie Chemical process control Mathematical optimization SCIENCE / Chemistry / Industrial & Technical bisacsh TECHNOLOGY & ENGINEERING / Electrical bisacsh Optimierung (DE-588)4043664-0 gnd Chemische Verfahrenstechnik (DE-588)4069941-9 gnd Technische Chemie (DE-588)4078178-1 gnd Prozessoptimierung (DE-588)4176074-8 gnd Prozessüberwachung (DE-588)4133922-8 gnd |
| subject_GND | (DE-588)4043664-0 (DE-588)4069941-9 (DE-588)4078178-1 (DE-588)4176074-8 (DE-588)4133922-8 |
| title | Optimal control for chemical engineers |
| title_auth | Optimal control for chemical engineers |
| title_exact_search | Optimal control for chemical engineers |
| title_full | Optimal control for chemical engineers Simant Ranjan Upreti |
| title_fullStr | Optimal control for chemical engineers Simant Ranjan Upreti |
| title_full_unstemmed | Optimal control for chemical engineers Simant Ranjan Upreti |
| title_short | Optimal control for chemical engineers |
| title_sort | optimal control for chemical engineers |
| topic | Chemie Chemical process control Mathematical optimization SCIENCE / Chemistry / Industrial & Technical bisacsh TECHNOLOGY & ENGINEERING / Electrical bisacsh Optimierung (DE-588)4043664-0 gnd Chemische Verfahrenstechnik (DE-588)4069941-9 gnd Technische Chemie (DE-588)4078178-1 gnd Prozessoptimierung (DE-588)4176074-8 gnd Prozessüberwachung (DE-588)4133922-8 gnd |
| topic_facet | Chemie Chemical process control Mathematical optimization SCIENCE / Chemistry / Industrial & Technical TECHNOLOGY & ENGINEERING / Electrical Optimierung Chemische Verfahrenstechnik Technische Chemie Prozessoptimierung Prozessüberwachung |
| url | https://www.doabooks.org/doab?func=fulltext&uiLanguage=en&rid=48330 https://www.doabooks.org/doab?func=fulltext&uiLanguage=en&rid=48420 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025433651&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025433651&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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