Linear optimal control:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Englewood Cliffs, N. J.
Prentice-Hall
1971
|
| Edition: | 1. print. |
| Series: | Prentice-Hall networks series
Prentice-Hall electrical engineering series |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 399 S. |
| ISBN: | 0135368707 |
Staff View
MARC
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Record in the Search Index
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| adam_text | CONTENTS
Part I
INTRODUCTION 1
Chapter 1 INTRODUCTION 3
1.1 Linear Optimal Control 3
1.2 About this Book in Particular 5
1.3 Part and Chapter Outline 6
Part II
BASIC THEORY OF
THE OPTIMAL REGULATOR 9
Chapter 2 THE STANDARD REGULATOR PROBLEM—I 11
2.1 A Review of the Regulator Problem 11
2.2 The Hamilton-Jacobi Equation 16
2.3 Solution of the Finite-Time Regulator Problem 23
Chapter 3 THE STANDARD REGULATOR PROBLEM—II 31
3.1 The Infinite-Time Regulator Problem 31
3.2 Stability of the Time-Invariant Regulator 39
3.3 Summary and Discussion of the Regulator Problem Results 43
3.4 Extensions of the Regulator Problem 46
xi
xii CONTENTS
Chapter 4 THE REGULATOR WITH A PRESCRIBED DEGREE
OF STABILITY 50
4.1 Qualitative Statement of the Regulator Problem with a
Prescribed Degree of Stability 50
4.2 Quantitative Statement and Solution of the Regulator
Problem with a Prescribed Degree of Stability 53
4.3 Extensions of the Preceding Results 59
Part III
PROPERTIES AND APPLICATION OF THE
OPTIMAL REGULATOR S3
Chapter 5 PROPERTIES OF REGULATOR SYSTEMS WITH A
CLASSICAL CONTROL INTERPRETATION 65
5.1 The Regulator from an Engineering Viewpoint 65
5.2 Some Fundamental Formulas 68
5.3 Gain Margin, Phase Margin and Time-delay Tolerance 70
5.4 Positioning of the Closed-Loop System Poles 77
Chapter 6 INSERTION OF NONLINEARITIES IN OPTIMAL
REGULATORS 91
6.1 Tolerance of Nonlinearities in the Feedback Loop 91
6.2 Relay Control Systems 99
6.3 Introduction of Relays into Nominally Optimal Systems 111
Chapter 7 SENSITIVITY ASPECTS OF OPTIMAL REGULATORS 117
7.1 The Sensitivity Problem 117
7.2 Sensitivity Reduction In Optimal Regulators 125
7.3 The Inverse Regulator Problem 135
7.4 Further Discussion of the Pole-Positioning Problem 141
Chapter 8 STATE ESTIMATOR DESIGN 145
8.1 The Nature of the State Estimation Problem 145
8.2 Nonstatistical Estimator Design with Full Estimator
Dimension 149
8.3 Nonstatistical Estimator Design with Reduced Estimator
Dynamics 159
8.4 Statistical Estimator Design (The Kalman-Bucy Filter) 169
CONTENTS xiii
Chapter 9 SYSTEM DESIGN USING STATE ESTIMATORS 192
9.1 Controller Design—Basic Versions 192
9.2 Variants on the Basic Controller 203
9.3 Simplifications of the Controller for Multiple-Output,
Single-Input Systems 212
9.4 The Separation Theorem 222
Part IV
EXTENSIONS TO
MORE COMPLEX PROBLEMS 225
Chapter 10 OPTIMAL LINEAR REGULATORS WITH INPUT
DISTURBANCES 227
10.1 Proportional-plus-Integral Feedback 227
10.2 The Regulator Problem with Derivative Constraints 229
10.3 Application and Properties of Optimal Regulators which
Include Integral Feedback 237
Chapter 11 TRACKING SYSTEMS 247
11.1 The Problem of Achieving a Desired Trajectory 247
11.2 Finite-Time Results 251
11.3 Infinite-Time Results 261
Chapter 12 OPTIMAL REGULATORS WITH DUAL-MODE
CONTROL 272
12.1 The Bang-Bang Mode and Linear Mode 272
12.2 Linear Mode Solutions to the Singular Optimal Control
Problem 282
12.3 Properties of the Dual-Mode Optimal Regulator 291
12.4 Optimal Regulator with Bounds on the Control
Derivative 299
Chapter 13 OPTIMAL LINEAR REGULATORS WITH CONTROLLER
CONSTRAINTS 303
13.1 Formulation of Specific Optimal Regulator Problems 303
13.2 Analytical Results and Computational Aspects 308
13.3 Properties of Optimal Solutions 316
13.4 Dynamic Controllers 321
Xiv CONTENTS
Chapter 14 TWO FURTHER TOPICS 328
14.1 Discrete Time Systems 328
14.2 The Infinite-Time Regulator Problem for Time-Varying
Systems 335
Part V
COMPUTATIONAL ASPECTS 341
Chapter 15 SOLUTION OF THE RICCATI EQUATION 343
15.1 Preliminary Remarks 343
15.2 Riccati Equation Solution with the Aid of a Linear
Differential Equation 345
15.3 Steady-State Solution of the Riccati Equation 353
15.4 Approximate Solutions of High-Order Riccati Equations
via Singular Perturbation 363
Appendix A BRIEF REVIEW OF SOME RESULTS OF MATRIX
THEORY 376
Appendix B BRIEF REVIEW OF SEVERAL MAJOR RESULTS
OF LINEAR SYSTEM THEORY 389
INDEX 393
|
| adam_txt |
CONTENTS
Part I
INTRODUCTION 1
Chapter 1 INTRODUCTION 3
1.1 Linear Optimal Control 3
1.2 About this Book in Particular 5
1.3 Part and Chapter Outline 6
Part II
BASIC THEORY OF
THE OPTIMAL REGULATOR 9
Chapter 2 THE STANDARD REGULATOR PROBLEM—I 11
2.1 A Review of the Regulator Problem 11
2.2 The Hamilton-Jacobi Equation 16
2.3 Solution of the Finite-Time Regulator Problem 23
Chapter 3 THE STANDARD REGULATOR PROBLEM—II 31
3.1 The Infinite-Time Regulator Problem 31
3.2 Stability of the Time-Invariant Regulator 39
3.3 Summary and Discussion of the Regulator Problem Results 43
3.4 Extensions of the Regulator Problem 46
xi
xii CONTENTS
Chapter 4 THE REGULATOR WITH A PRESCRIBED DEGREE
OF STABILITY 50
4.1 Qualitative Statement of the Regulator Problem with a
Prescribed Degree of Stability 50
4.2 Quantitative Statement and Solution of the Regulator
Problem with a Prescribed Degree of Stability 53
4.3 Extensions of the Preceding Results 59
Part III
PROPERTIES AND APPLICATION OF THE
OPTIMAL REGULATOR S3
Chapter 5 PROPERTIES OF REGULATOR SYSTEMS WITH A
CLASSICAL CONTROL INTERPRETATION 65
5.1 The Regulator from an Engineering Viewpoint 65
5.2 Some Fundamental Formulas 68
5.3 Gain Margin, Phase Margin and Time-delay Tolerance 70
5.4 Positioning of the Closed-Loop System Poles 77
Chapter 6 INSERTION OF NONLINEARITIES IN OPTIMAL
REGULATORS 91
6.1 Tolerance of Nonlinearities in the Feedback Loop 91
6.2 Relay Control Systems 99
6.3 Introduction of Relays into Nominally Optimal Systems 111
Chapter 7 SENSITIVITY ASPECTS OF OPTIMAL REGULATORS 117
7.1 The Sensitivity Problem 117
7.2 Sensitivity Reduction In Optimal Regulators 125
7.3 The Inverse Regulator Problem 135
7.4 Further Discussion of the Pole-Positioning Problem 141
Chapter 8 STATE ESTIMATOR DESIGN 145
8.1 The Nature of the State Estimation Problem 145
8.2 Nonstatistical Estimator Design with Full Estimator
Dimension 149
8.3 Nonstatistical Estimator Design with Reduced Estimator
Dynamics 159
8.4 Statistical Estimator Design (The Kalman-Bucy Filter) 169
CONTENTS xiii
Chapter 9 SYSTEM DESIGN USING STATE ESTIMATORS 192
9.1 Controller Design—Basic Versions 192
9.2 Variants on the Basic Controller 203
9.3 Simplifications of the Controller for Multiple-Output,
Single-Input Systems 212
9.4 The Separation Theorem 222
Part IV
EXTENSIONS TO
MORE COMPLEX PROBLEMS 225
Chapter 10 OPTIMAL LINEAR REGULATORS WITH INPUT
DISTURBANCES 227
10.1 Proportional-plus-Integral Feedback 227
10.2 The Regulator Problem with Derivative Constraints 229
10.3 Application and Properties of Optimal Regulators which
Include Integral Feedback 237
Chapter 11 TRACKING SYSTEMS 247
11.1 The Problem of Achieving a Desired Trajectory 247
11.2 Finite-Time Results 251
11.3 Infinite-Time Results 261
Chapter 12 OPTIMAL REGULATORS WITH DUAL-MODE
CONTROL 272
12.1 The Bang-Bang Mode and Linear Mode 272
12.2 Linear Mode Solutions to the Singular Optimal Control
Problem 282
12.3 Properties of the Dual-Mode Optimal Regulator 291
12.4 Optimal Regulator with Bounds on the Control
Derivative 299
Chapter 13 OPTIMAL LINEAR REGULATORS WITH CONTROLLER
CONSTRAINTS 303
13.1 Formulation of Specific Optimal Regulator Problems 303
13.2 Analytical Results and Computational Aspects 308
13.3 Properties of Optimal Solutions 316
13.4 Dynamic Controllers 321
Xiv CONTENTS
Chapter 14 TWO FURTHER TOPICS 328
14.1 Discrete Time Systems 328
14.2 The Infinite-Time Regulator Problem for Time-Varying
Systems 335
Part V
COMPUTATIONAL ASPECTS 341
Chapter 15 SOLUTION OF THE RICCATI EQUATION 343
15.1 Preliminary Remarks 343
15.2 Riccati Equation Solution with the Aid of a Linear
Differential Equation 345
15.3 Steady-State Solution of the Riccati Equation 353
15.4 Approximate Solutions of High-Order Riccati Equations
via Singular Perturbation 363
Appendix A BRIEF REVIEW OF SOME RESULTS OF MATRIX
THEORY 376
Appendix B BRIEF REVIEW OF SEVERAL MAJOR RESULTS
OF LINEAR SYSTEM THEORY 389
INDEX 393 |
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| illustrated | Not Illustrated |
| index_date | 2024-07-02T16:05:32Z |
| indexdate | 2024-07-09T20:47:20Z |
| institution | BVB |
| isbn | 0135368707 |
| language | English |
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| owner_facet | DE-706 |
| physical | 399 S. |
| publishDate | 1971 |
| publishDateSearch | 1971 |
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| publisher | Prentice-Hall |
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| series2 | Prentice-Hall networks series Prentice-Hall electrical engineering series |
| spelling | Anderson, Brian D. O. 1949- Verfasser (DE-588)122209478 aut Linear optimal control Brian D. O. Anderson ; John B. Moore 1. print. Englewood Cliffs, N. J. Prentice-Hall 1971 399 S. txt rdacontent n rdamedia nc rdacarrier Prentice-Hall networks series Prentice-Hall electrical engineering series Commande, Théorie de la Control theory Kontrolltheorie (DE-588)4032317-1 gnd rswk-swf Lineare Regelung (DE-588)4035819-7 gnd rswk-swf Lineare Regelung (DE-588)4035819-7 s DE-604 Kontrolltheorie (DE-588)4032317-1 s 1\p DE-604 Moore, John Bassett 1860-1947 Verfasser (DE-588)117601179 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015131730&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Anderson, Brian D. O. 1949- Moore, John Bassett 1860-1947 Linear optimal control Commande, Théorie de la Control theory Kontrolltheorie (DE-588)4032317-1 gnd Lineare Regelung (DE-588)4035819-7 gnd |
| subject_GND | (DE-588)4032317-1 (DE-588)4035819-7 |
| title | Linear optimal control |
| title_auth | Linear optimal control |
| title_exact_search | Linear optimal control |
| title_exact_search_txtP | Linear optimal control |
| title_full | Linear optimal control Brian D. O. Anderson ; John B. Moore |
| title_fullStr | Linear optimal control Brian D. O. Anderson ; John B. Moore |
| title_full_unstemmed | Linear optimal control Brian D. O. Anderson ; John B. Moore |
| title_short | Linear optimal control |
| title_sort | linear optimal control |
| topic | Commande, Théorie de la Control theory Kontrolltheorie (DE-588)4032317-1 gnd Lineare Regelung (DE-588)4035819-7 gnd |
| topic_facet | Commande, Théorie de la Control theory Kontrolltheorie Lineare Regelung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015131730&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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