Control of indefinite nonlinear dynamic systems: induced internal feedback
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
London ; Berlin ; Heidelberg ; New York ; Barcelona ; Budapest ;
Springer
1998
|
| Series: | Lecture notes in control and information sciences
231 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus dem Russ. übers. |
| Physical Description: | XIII, 196 S. graph. Darst. |
| ISBN: | 3540762450 |
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MARC
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Record in the Search Index
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| adam_text | Contents
Preface xi
Chapter 1. Introduction l
Section 1. Processes, Systems, Actions: General Issues 1
1.1. What Do We Want? 1
1.2. What Can the Interrelation between Processes Afford? 1
1.3. Language of the General Theory of Systems 2
1.4. A System and an Object 3
1.5. Transfer of Actions Through the Chain of Systems 4
1.6. Direct Actions: A Small Trap 5
1.7. Sources of Actions 6
1.8. Is There a Need for an Intermediate System 8
Section 2. Practice: Survey of Examples 9
2.1. Biology: The Predator Victim System 9
2.2. Power Engineering: An Atomic Power Plant 10
2.3. Economics: Nationed Market Economy and State Budget 10
2.4. Production Engineering:
Chemical Interaction Between Two Reagents 11
2.5. Medicine: Hormonotherapy for Diabetes 12
2.6. Mechanics: Irregular Rectilinear Motion 12
Section 3. Mathematical Tools and the Subject of Study 13
3.1. How Can We Turn from Words to Deeds? 14
3.2. Why Did We Turn to Differential Equations? 15
3.3. Indeterminate Differential Equations 16
3.4. Language of the Theory of Automatic Control 17
3.5. What is a Dynamic System? 17
3.6. Differential Equations as Models of Dynamic Systems 18
3.7. Model of a Controllable Object 20
3.8. Control Problems: How to Handle Them 21
Chapter 2. Control of Elementary Dynamic Systems 23
Section 4. Control of a One Dimensional Object 23
4.1. Model of an Object and Control Capabilities 23
vi Contents
4.2. What Can a Majorant Do? 24
4.3. Problem of Correctness
and Completion of Control Synthesis 25
4.4. Character of Transient Processes 28
4.5. Extension of the Problem:
An Indeterminate Coefficient Involved with a Control Action.. 30
4.6. Extension of the Problem: Additional State Parameters 30
4.7. Extension of the Problem: Variable Control Accuracy 31
4.8. Prospects of Further Extensions 32
Section 5. Control of a Nonlinear Multidimensional Object 32
5.1. Model of the Object and Discussion of the Problem 32
5.2. Lyapunov Function 33
5.3. What Norm Must We Select? 34
5.4. Control Synthesis 35
5.5. Character of Transient Processes 36
5.6. Possibilities for Extension of the Problem 37
5.7. Comments on the Control Law 37
Chapter 3. Control Problem for an Intermediate Link 39
Section 6. Results — Predecessors 39
6.1. Statement of the Problem:
Remote and Immediate Objectives of Control 40
6.2. Linear Control 41
6.3. Strong Feedback 42
6.4. Bounded Actions 43
6.5. Varying Structure System 45
6.6. Dynamic Binary Control 46
Section 7. New Properties of Two Dimensional Problems 48
7.1. Discussion of Statement of the Problem 48
7.2. Control Synthesis 49
7.3. Correctness Problem 50
7.4. Control in the General Case 50
7.5. Behavior of Solutions 50
7.6. Some Remarks 52
Section 8. Internal Feedback 53
8.1. Natural Control Loops 53
8.2. Internal Feedback and Control Problems 54
8.3. Induced Internal Feedback 57
8.4. Induction with Error 58
Contents vii
8.5. Chains of Induction Problems 60
8.6. Clusters of Induction Problems 61
8.7. What is the Need for so Many Problems? 63
Section 9. Synthesis of the Induction Control 64
9.1. Statement of the Induction Problem 64
9.2. Concept of Control Synthesis 67
9.3. Control Law 68
9.4. What Else Is to Be Done? 69
Section 10. Correctness of the Closed System 70
10.1. Continuity of the Control 70
10.2. The Lipschitz Condition 72
10.3. Summary of the Results 74
Section 11. The System with Induced Feedback:
General Properties of Trajectories 74
11.1. Variation of an Induction Error 74
11.2. Induction Conditions for Desired Feedback 76
11.3. Do We Need Exceptional Trajectories? 78
11.4. Hyperbolic Asymptotics 80
11.5. Exponential Asymptotics 81
11.6. Summary of the Results 82
Section 12. Control Synthesis Errors and their Aftereffects 83
12.1. Errors Localized in a Certain Domain 83
12.2. Underestimation of Model Parameters 84
12.3. It There Any Need to Find our Errors? 86
Section 13. Values of the Control Actions in the Induction System 87
13.1. What Do We Need to Study? 87
13.2. The One Dimensional Linear Example 88
13.3. A High Coefficient in the Induction Control 89
13.4. A Varying High Coefficient 91
13.5. What Is to Be Done
to Effect Savings in Control from the Outset? 93
13.6. A Fly in the Ointment 94
13.7. Basic Result 95
Section 14. Potential Functions of Induction Control 96
14.1. Potential Systems. Levels of Clarity of Representation 96
14.2. Construction of the Potential Function of Control 97
14.3. Interpretation of Common Properties of Trajectories 99
14.4. Aftereffects of Errors and Results of Preventive Measures 99
viii Contents
Section 15. Structure of the Induction System 100
15.1. Language of Block Diagrams 100
15.2. Block Diagrams of Controllable Systems 102
15.3. Structure of the Control Law 105
15.4. What is a Binary System? 106
Chapter 4. Construction of Tracking Systems 109
Section 16. Tracking Systems with Multilevel Binary Structures 109
16.1. Induction Control in the Tracking System 110
16.2. How to State the Induction Problem? Ill
16.3. Generation of Inducing Feedback 112
16.4. Construction of the Control System 114
16.5. Multilevel Binary Structure 116
16.6. Operation of the Multilevel System 117
Section 17. Ways of Extending the Capabilities of the Approach 120
17.1. Oscillations in Tracking Systems 121
17.2. Oscillations in Induction Systems 122
17.3. Ways of Eliminating Oscillations 124
17.4. Termwise Induction and a New Class of Problems 127
Section 18. Termwise Induction in Systems with Branching Structures . 127
18.1. General Design Considerations 128
18.2. Statement of the Termwise Induction Problem 129
18.3. Synthesis and Properties of the Control Algorithm 130
18.4. Structure Representation 131
18.5. Termwise Induction in Tracking Systems 132
18.6. Intact Clusters 135
Chapter 5. Induction Control. Practical Examples 137
Section 19. Biology: Control of Predator Victim Systems 138
19.1. Discussion of Practical Issues 138
19.2. Model of the Predator Victim Biocenosis 139
19.3. Reproduction of Predators for Annihilation of Victims 141
19.4. Where Is it Possible to Stabilize Predator Victim Systems? ... 144
19.5. Stabilization of Systems
Involving Reproduction of Predators 145
19.6. Stabilization of Systems Involving Removal of Predators 147
19.7. Stabilization of Systems Involving Removal of Victims 148
19.8. Stabilization of Systems
by Removal of Predators and Victims 150
Contents ix
Section 20. Power Engineering: Control of a Nuclear Reactor 152
20.1. Why Does the Nuclear Reactor Heat up? 152
20.2. Chain Reaction 153
20.3. Existence of a Neutron 154
20.4. Populations of Neutrons 156
20.5. Mathematical Model of the Reactor 158
20.6. Statement of the Problem and Properties of the Model 159
20.7. Why Must the Control be Nonlinear? 161
20.8. Construction of the Control Law 162
20.9. Properties of the Closed System 163
Section 21. Economy: Stabilization of the Trajectories of Growth 165
21.1. On Modeling of Economic Systems 165
21.2. Essence of Processes Under Study 166
21.3. Equations of the Model 167
21.4. Labor Force and Constraints on Variables 169
21.5. Economic Growth and Statement of the Problem 170
21.6. Linear Control and the Uncertainty Problem 172
21.7. Control of Unemployment as Induction 172
21.8. Induction Control 173
21.9. Comments on the Results 174
Section 22. Technology: Control of an Exothermic Reaction 175
22.1. Production Process and the Control Problem 175
22.2. Mathematical Model of the Process 176
22.3. Statement of the Control Problem 178
22.4. Statement of the Induction Problem 179
22.5. Synthesis of the Induction Control 181
22.6. Constraints and Drawbacks 182
Section 23. Medicine:
Control of Carbohydrate Metabolism for Diabetes 183
23.1. Carbohydrate Metabolism and Insulin Dependent Diabetes... 183
23.2. Mathematical Model of Carbohydrate Metabolism 184
23.3. Constraints on Variables and Statement of the Problem 186
23.4. Is Diabetes Doomed? 187
23.5. Synthesis of the Control 188
23.6. Properties of the Closed System 190
Conclusion 191
Bibliography 193
|
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:17:52Z |
| institution | BVB |
| isbn | 3540762450 |
| language | German |
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| physical | XIII, 196 S. graph. Darst. |
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| publisher | Springer |
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| series | Lecture notes in control and information sciences |
| series2 | Lecture notes in control and information sciences |
| spelling | Emelʹjanov, Stanislav V. 1929- Verfasser (DE-588)121848981 aut Control of indefinite nonlinear dynamic systems induced internal feedback S. V. Emel'yanov, I. A. Burovoi and F. Yu. Levada London ; Berlin ; Heidelberg ; New York ; Barcelona ; Budapest ; Springer 1998 XIII, 196 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in control and information sciences 231 Aus dem Russ. übers. Nichtlineare Kontrolltheorie Nichtlineares dynamisches System - Rückkopplung Nichtlineares dynamisches System (DE-588)4126142-2 gnd rswk-swf Nichtlineare Kontrolltheorie (DE-588)4475218-0 gnd rswk-swf Rückkopplung (DE-588)4050851-1 gnd rswk-swf Nichtlineares dynamisches System (DE-588)4126142-2 s Rückkopplung (DE-588)4050851-1 s DE-604 Nichtlineare Kontrolltheorie (DE-588)4475218-0 s Burovoij, Isaac A. Verfasser aut Levada, Fedor J. Verfasser aut Lecture notes in control and information sciences 231 (DE-604)BV005848579 231 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008024526&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Emelʹjanov, Stanislav V. 1929- Burovoij, Isaac A. Levada, Fedor J. Control of indefinite nonlinear dynamic systems induced internal feedback Lecture notes in control and information sciences Nichtlineare Kontrolltheorie Nichtlineares dynamisches System - Rückkopplung Nichtlineares dynamisches System (DE-588)4126142-2 gnd Nichtlineare Kontrolltheorie (DE-588)4475218-0 gnd Rückkopplung (DE-588)4050851-1 gnd |
| subject_GND | (DE-588)4126142-2 (DE-588)4475218-0 (DE-588)4050851-1 |
| title | Control of indefinite nonlinear dynamic systems induced internal feedback |
| title_auth | Control of indefinite nonlinear dynamic systems induced internal feedback |
| title_exact_search | Control of indefinite nonlinear dynamic systems induced internal feedback |
| title_full | Control of indefinite nonlinear dynamic systems induced internal feedback S. V. Emel'yanov, I. A. Burovoi and F. Yu. Levada |
| title_fullStr | Control of indefinite nonlinear dynamic systems induced internal feedback S. V. Emel'yanov, I. A. Burovoi and F. Yu. Levada |
| title_full_unstemmed | Control of indefinite nonlinear dynamic systems induced internal feedback S. V. Emel'yanov, I. A. Burovoi and F. Yu. Levada |
| title_short | Control of indefinite nonlinear dynamic systems |
| title_sort | control of indefinite nonlinear dynamic systems induced internal feedback |
| title_sub | induced internal feedback |
| topic | Nichtlineare Kontrolltheorie Nichtlineares dynamisches System - Rückkopplung Nichtlineares dynamisches System (DE-588)4126142-2 gnd Nichtlineare Kontrolltheorie (DE-588)4475218-0 gnd Rückkopplung (DE-588)4050851-1 gnd |
| topic_facet | Nichtlineare Kontrolltheorie Nichtlineares dynamisches System - Rückkopplung Nichtlineares dynamisches System Rückkopplung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008024526&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV005848579 |
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