Dynamic systems and control with applications:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Hackensack, NJ [u.a.]
World Scientific
2006
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 450 S. |
| ISBN: | 9812700536 |
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MARC
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| 100 | 1 | |a Ahmed, Nasir Uddin |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Dynamic systems and control with applications |c N.U. Ahmed |
| 264 | 1 | |a Hackensack, NJ [u.a.] |b World Scientific |c 2006 | |
| 300 | |a XV, 450 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Control theory | |
| 650 | 4 | |a System theory | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-016173372 | ||
Record in the Search Index
| _version_ | 1804137219992059904 |
|---|---|
| adam_text | Contents
Preface
xiii
1 Basic
Mathematical Background
1
1.1
Introduction
............................ 1
1.2
Vector Space
........................... 1
1.3
Normed Space
........................... 2
1.4
Banach Space
........................... 6
1.4.1
Hilbert Space
....................... 7
1.4.2
Special Banach Spaces
.................. 9
1.5
Metric Space
........................... 16
1.6
Banach Fixed Point Theorems
................. 22
1.7
Bibliographical Notes
....................... 28
2
Linear Systems
29
2.1
Introduction
............................ 29
2.2
Some Examples
.......................... 30
2.3
Representation of Solutions for
TIS
............... 36
2.4
Representation of Solutions for TVS
.............. 43
2.5
Continuous Dependence of Solution on Data
.......... 51
2.6
Input-Output Stability and System Equivalence
........ 54
2.7
Impulsive (Measure Driven) Systems
.............. 63
2.7.1
Systems Subject to Impulsive Inputs
.......... 64
2.7.2
Systems Subject to Impulsive Structural
Perturbation
....................... 67
2.7.3
Controlled Impulsive Systems
.............. 72
2.8
Exercises
............................. 73
2.9
Bibliographical Notes
....................... 74
3
Nonlinear Systems
77
3.1
Introduction
............................ 77
3.2
Some Examples
.......................... 77
3.3
Existence and Uniqueness of Solutions
............. 79
3.4
Properties of Solution Operator
................. 87
3.5
Continuous Dependence of Solutions
.............. 89
3.6
Impulsive Systems
........................ 94
3.6.1
Classical Models
..................... 95
3.6.2
General Impulsive Models (Driven by
Vector Measures)
..................... 102
3.7
Differential Inclusions
...................... 108
3.8
Exercises
............................. 115
3.9
Bibliographical Notes
....................... 116
4
Basic Stability Theory
119
4.1
Introduction
............................ 119
4.2
Stability of the Equilibrium
................... 120
4.3
Lyapunov Stability Theory
................... 124
4.4
Lyapunov First Method
...................... 133
4.5
Stability of Elementary Impulsive Systems
........... 140
4.6
Exercises
............................. 148
4.7
Bibliographical Notes
....................... 150
5
Observability and Identification
151
5.1
Introduction
............................ 151
5.2
Linear Time Invariant Systems
................. 151
5.3
Some Examples
.......................... 159
5.4
Linear Time Varying Systems
.................. 162
5.5
Input Identification
........................ 167
5.6
Exercises
............................. 178
5.7
Bibliographical Notes
....................... 179
6
Controllability and Stabilizability
181
6.1
Introduction
............................ 181
6.2
Linear Time Invariant Systems
................. 181
6.3
Linear Time Varying Systems
.................. 194
6.4
Perturbed (Linear/Nonlinear) Systems
............. 200
6.5
Stabilizability and Dynamic Compensators
.......... 208
6.6
Controllability of Linear Impulsive Systems
.......... 215
6.7
Exercises
............................. 218
6.8
Bibliographical
Notes
....................... 219
7
Basic
Calculus of
Variations
221
7.1
Introduction
............................ 221
7.2
Finite Dimensional Problems
.................. 221
7.3
Existence of Solutions for Variational Problems
........ 224
7.4
Necessary Conditions
....................... 238
7.5
Basic Algorithm for Numerical Computation
......... 246
7.6
Some Examples
.......................... 248
7.7
Exercises
............................. 252
7.8
Bibligraphical Notes
....................... 253
8
Optimal Control: Necessary Conditions and Existence
255
8.1
Introduction
............................ 255
8.2
General Problem
......................... 255
8.3
Necessary Conditions of Optimality
............... 257
8.3.1
Ordinary Controls
.................... 257
8.3.2
Transvèrsality
Conditions:
................ 267
8.3.3
Relaxed Controls
..................... 271
8.4
Some Special Cases involving constraints
............ 280
8.5
Basic Algorithm for Numerical Computation
......... 283
8.6
Existence of Optimal Controls
.................. 285
8.6.1
Ordinary Controls
.................... 285
8.6.2
Relaxed Controls
..................... 290
8.6.3
Uncertain Systems/Differential Inclusions
....... 293
8.6.4
Impulsive Controls
.................... 297
8.7
Exercises
............................. 299
8.8
Bibliographical Notes
....................... 301
9
Linear Quadratic Regulator Theory
303
9.1
Introduction
............................ 303
9.2
Linear Quadratic Regulator
................... 304
9.3
Perturbed Regulators
...................... 312
9.4
Constrained Regulators
...................... 314
9.5
Algebraic Riccati Equation: Steady State
........... 316
9.6
Some
Nonstandard
Regulator Problems
............ 320
9.7
Disturbance Rejection Problem
................. 328
9.8
Structurally Perturbed Impulsive Systems
........... 330
9.9
Exercises
............................. 335
9.10
Bibliographical Notes
....................... 335
10
Time Optimal Control
337
10.1
Introduction
............................ 337
10.2
General Problem
......................... 337
10.3
Attainable and Reachable Sets
................. 338
10.4
Linear Systems
.......................... 338
10.4.1
Bang-Bang Control
.................... 343
10.5
Linear Impulsive Systems
.................... 348
10.6
Nonlinear Systems Including an Algorithm
........... 350
10.7
Exercises
............................. 356
10.8
Bibliographical Notes
....................... 357
11
Stochastic Systems with Applications
359
11.1
Introduction
............................ 359
11.2
Stochastic Systems
........................ 359
11.2.1
SDE Based on Brownian Motion
............ 360
11.2.2
SDE Based on Fractional Brownian Motion
...... 369
11.3
Differential Equations Based on
Poisson
Process
....... 373
11.3.1
Application to Auto-Insurance
............. 377
11.3.2
Application to Portfolio Management
......... 379
11.3.3
Population Dynamics
.................. 382
11.4
Applications to Computer Network
............... 383
11.4.1
Dynamic Model for Access Control
........... 384
11.4.2
TCP Flow Control and Active Queue
Management
....................... 390
11.5
Real Time Control and Optimization
.............. 398
11.5.1
Deterministic System
.................. 398
11.5.2
Stochastic System
.................... 400
11.6
Exercises
............................. 402
11.7
Bibliographical Notes
....................... 403
A Basic Results from Analysis
405
A.I Introduction
............................ 405
A.
2
Measures and Measurable Functions
.............. 405
A.3 Riemann and Riemann-Stieltjes Integral
............ 407
A.4 Lebesgue Integral
......................... 408
A.
5
Modes of Convergence
...................... 411
Contents xi
Α.
6
Frequently Used Results from Measure Theory
........414
A.
7
Frequently Used Results from Analysis
.............423
A.8 Bibliographical Notes
.......................427
Bibliography
429
Index
447
|
| adam_txt |
Contents
Preface
xiii
1 Basic
Mathematical Background
1
1.1
Introduction
. 1
1.2
Vector Space
. 1
1.3
Normed Space
. 2
1.4
Banach Space
. 6
1.4.1
Hilbert Space
. 7
1.4.2
Special Banach Spaces
. 9
1.5
Metric Space
. 16
1.6
Banach Fixed Point Theorems
. 22
1.7
Bibliographical Notes
. 28
2
Linear Systems
29
2.1
Introduction
. 29
2.2
Some Examples
. 30
2.3
Representation of Solutions for
TIS
. 36
2.4
Representation of Solutions for TVS
. 43
2.5
Continuous Dependence of Solution on Data
. 51
2.6
Input-Output Stability and System Equivalence
. 54
2.7
Impulsive (Measure Driven) Systems
. 63
2.7.1
Systems Subject to Impulsive Inputs
. 64
2.7.2
Systems Subject to Impulsive Structural
Perturbation
. 67
2.7.3
Controlled Impulsive Systems
. 72
2.8
Exercises
. 73
2.9
Bibliographical Notes
. 74
3
Nonlinear Systems
77
3.1
Introduction
. 77
3.2
Some Examples
. 77
3.3
Existence and Uniqueness of Solutions
. 79
3.4
Properties of Solution Operator
. 87
3.5
Continuous Dependence of Solutions
. 89
3.6
Impulsive Systems
. 94
3.6.1
Classical Models
. 95
3.6.2
General Impulsive Models (Driven by
Vector Measures)
. 102
3.7
Differential Inclusions
. 108
3.8
Exercises
. 115
3.9
Bibliographical Notes
. 116
4
Basic Stability Theory
119
4.1
Introduction
. 119
4.2
Stability of the Equilibrium
. 120
4.3
Lyapunov Stability Theory
. 124
4.4
Lyapunov First Method
. 133
4.5
Stability of Elementary Impulsive Systems
. 140
4.6
Exercises
. 148
4.7
Bibliographical Notes
. 150
5
Observability and Identification
151
5.1
Introduction
. 151
5.2
Linear Time Invariant Systems
. 151
5.3
Some Examples
. 159
5.4
Linear Time Varying Systems
. 162
5.5
Input Identification
. 167
5.6
Exercises
. 178
5.7
Bibliographical Notes
. 179
6
Controllability and Stabilizability
181
6.1
Introduction
. 181
6.2
Linear Time Invariant Systems
. 181
6.3
Linear Time Varying Systems
. 194
6.4
Perturbed (Linear/Nonlinear) Systems
. 200
6.5
Stabilizability and Dynamic Compensators
. 208
6.6
Controllability of Linear Impulsive Systems
. 215
6.7
Exercises
. 218
6.8
Bibliographical
Notes
. 219
7
Basic
Calculus of
Variations
221
7.1
Introduction
. 221
7.2
Finite Dimensional Problems
. 221
7.3
Existence of Solutions for Variational Problems
. 224
7.4
Necessary Conditions
. 238
7.5
Basic Algorithm for Numerical Computation
. 246
7.6
Some Examples
. 248
7.7
Exercises
. 252
7.8
Bibligraphical Notes
. 253
8
Optimal Control: Necessary Conditions and Existence
255
8.1
Introduction
. 255
8.2
General Problem
. 255
8.3
Necessary Conditions of Optimality
. 257
8.3.1
Ordinary Controls
. 257
8.3.2
Transvèrsality
Conditions:
. 267
8.3.3
Relaxed Controls
. 271
8.4
Some Special Cases involving constraints
. 280
8.5
Basic Algorithm for Numerical Computation
. 283
8.6
Existence of Optimal Controls
. 285
8.6.1
Ordinary Controls
. 285
8.6.2
Relaxed Controls
. 290
8.6.3
Uncertain Systems/Differential Inclusions
. 293
8.6.4
Impulsive Controls
. 297
8.7
Exercises
. 299
8.8
Bibliographical Notes
. 301
9
Linear Quadratic Regulator Theory
303
9.1
Introduction
. 303
9.2
Linear Quadratic Regulator
. 304
9.3
Perturbed Regulators
. 312
9.4
Constrained Regulators
. 314
9.5
Algebraic Riccati Equation: Steady State
. 316
9.6
Some
Nonstandard
Regulator Problems
. 320
9.7
Disturbance Rejection Problem
. 328
9.8
Structurally Perturbed Impulsive Systems
. 330
9.9
Exercises
. 335
9.10
Bibliographical Notes
. 335
10
Time Optimal Control
337
10.1
Introduction
. 337
10.2
General Problem
. 337
10.3
Attainable and Reachable Sets
. 338
10.4
Linear Systems
. 338
10.4.1
Bang-Bang Control
. 343
10.5
Linear Impulsive Systems
. 348
10.6
Nonlinear Systems Including an Algorithm
. 350
10.7
Exercises
. 356
10.8
Bibliographical Notes
. 357
11
Stochastic Systems with Applications
359
11.1
Introduction
. 359
11.2
Stochastic Systems
. 359
11.2.1
SDE Based on Brownian Motion
. 360
11.2.2
SDE Based on Fractional Brownian Motion
. 369
11.3
Differential Equations Based on
Poisson
Process
. 373
11.3.1
Application to Auto-Insurance
. 377
11.3.2
Application to Portfolio Management
. 379
11.3.3
Population Dynamics
. 382
11.4
Applications to Computer Network
. 383
11.4.1
Dynamic Model for Access Control
. 384
11.4.2
TCP Flow Control and Active Queue
Management
. 390
11.5
Real Time Control and Optimization
. 398
11.5.1
Deterministic System
. 398
11.5.2
Stochastic System
. 400
11.6
Exercises
. 402
11.7
Bibliographical Notes
. 403
A Basic Results from Analysis
405
A.I Introduction
. 405
A.
2
Measures and Measurable Functions
. 405
A.3 Riemann and Riemann-Stieltjes Integral
. 407
A.4 Lebesgue Integral
. 408
A.
5
Modes of Convergence
. 411
Contents xi
Α.
6
Frequently Used Results from Measure Theory
.414
A.
7
Frequently Used Results from Analysis
.423
A.8 Bibliographical Notes
.427
Bibliography
429
Index
447 |
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| index_date | 2024-07-02T19:07:49Z |
| indexdate | 2024-07-09T21:08:49Z |
| institution | BVB |
| isbn | 9812700536 |
| language | English |
| lccn | 2007271049 |
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| spelling | Ahmed, Nasir Uddin Verfasser aut Dynamic systems and control with applications N.U. Ahmed Hackensack, NJ [u.a.] World Scientific 2006 XV, 450 S. txt rdacontent n rdamedia nc rdacarrier Control theory System theory Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016173372&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ahmed, Nasir Uddin Dynamic systems and control with applications Control theory System theory |
| title | Dynamic systems and control with applications |
| title_auth | Dynamic systems and control with applications |
| title_exact_search | Dynamic systems and control with applications |
| title_exact_search_txtP | Dynamic systems and control with applications |
| title_full | Dynamic systems and control with applications N.U. Ahmed |
| title_fullStr | Dynamic systems and control with applications N.U. Ahmed |
| title_full_unstemmed | Dynamic systems and control with applications N.U. Ahmed |
| title_short | Dynamic systems and control with applications |
| title_sort | dynamic systems and control with applications |
| topic | Control theory System theory |
| topic_facet | Control theory System theory |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016173372&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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