Systems: Decomposition, optimisation and control:
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Oxford
Pergamon Press
1978
|
| Schriftenreihe: | Pergamon international library of science, technology, engineering and social studies.
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XV, 645 S. graph. Darst. |
| ISBN: | 0080221505 |
Internformat
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| 245 | 1 | 0 | |a Systems: Decomposition, optimisation and control |c ed. by M. G. Singh ... |
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Datensatz im Suchindex
| _version_ | 1804116757866086400 |
|---|---|
| adam_text | Contents
page
Acknowledgements 1
Preface 3
PART 1 : STATIC OPTIMISATION 5
Chapter 1 : INTRODUCTION 5
1.1 General notions of control of processes 5
1.1.1 The control problem 5
1.1.2 Mathematical models and identification 9
1.1.3 Optimisation methods 11
1.1.4 Synthesis of the control system 13
1.2 Evolution of Systems Engineering Techniques to solve
complex System problems 14
1.2.1 Introduction 14
1.2.2 Analysis 15
1.2.3 Aggregation 17
1.2.4 Decomposition or partitioning of complex systems 17
1.2.5 General principles of hierarchical control 18
1.2.5.1 The multi level multi objective structure 18
1.2.5.2 Division of labour 20
1.2.5.3 Coordination 21
1.3 Mathematical generalities for mathematical programming 25
1.3.1 Aim of mathematical programming 25
1.3.2 Some elementary mathematical concepts 28
1.4 Conclusions 34
References for chapter 1 35
Chapter 2 : LINEAR PROGRAMMING 37
2.1 Basic concepts : introductory examples 37
2.1.1 Example 1 37
2.1.2 Example 2 39
2.2 The Simplex Method 40
2.2.1 Putting Linear Programs into the standard form 40
2.2.1.1 Putting into the standard form 40
2.2.1.2 Basic theorems of linear programming 42
2.2.1.3 Linear systems of equations and equivalent
systems 44
2.2.2 The Simplex Algorithm 46
2.2.2.1 Optimality Test 47
vii
via
2.2.2.2 Improvement of a non optimal basic
solution : an example 47
2.2.2.3 Improvement of a non optimal but feasible
basic solution : general case 50
2.2.3 The two phases ot the Simplex Method 51
2.2.4 Examples of linear programming 52
2.3 The Revised Simplex Method 55
2.4 Duality in linear programming 62
2.5 The Dantzig Wolfedecomposition algorithm 63
2.6 Conclusions 67
References for chapter 2 68
Problems for chapter 2 69
Chapter 3 : NON LINEAR PROGRAMMING 71
3.1 Seeking the Minimum for Unconstrained Problems 71
3.1.1 First order conditions 71
3.1.2 Second order conditions 72
3.1.3 Iterative search methods 73
3.1.3.1 Gradient method 73
3.1.3.2 Newton s method 74
3.1.3.3 Convergence of the Gradient method and
Newton s method 75
3.1.4 A few additional algorithms 79
3.1.4.1 Simplified algorithms 79
3.1.4.2 The PARTAN method 81
3.1.4.3 Algorithms having a quadratic final
convergence 83
3.1.4.4 Choice of the algorithm to be used 84
3.2 Minimisation subject to Equality constraints 86
3.2.1 First order conditions 86
3.2.2 Second order conditions 88
3.2.3 Minmax Formula 93
3.2.4 The Gradient method 94
3.2.4.1 The aim of the algorithm 94
3.2.4.2 Geometric interpretation 95
3.2.4.3 Constraint handling 96
3.2.5 Newton s method 97
3.2.6 Penalty function 99
3.3 Minimisation subject to Inequality constraints 100
3.3.1 First order conditions 100
3.3.2 Second order conditions 101
3.3.3 The case of convex functions 103
3.3.3.1 Necessary and sufficient conditions for
to be convex 103
3.3.3.2 Minimum of a convex function on a convex set 104
ix
3.3.4 The Minmax Formula 104
3.3.5 Examples 105
3.3.6 The Gradient method 108
3.3.7 Other approaches 112
3.3.7.1 Use of penalty functions 112
3.3.7.2 The Arrow Hurwicz method 113
3.4 Application of Mathematical programming to solve control
problems 114
3.4.1 Theoretical optimality conditions 114
3.4.1.1 The problem 114
3.4.1.2 Necessary conditions for optimality 115
3.4.2 The practical search for an optimal solution 117
3.4.2.1 Solution of the Recursive equations 118
3.4.2.2 The boundary conditions 119
3.5 Conclusions 120
References for chapter 3 121
Problems for chapter 3 122
Chapter 4 : DECOMPOSITION COORDINATION METHODS IN NON LINEAR PROGRAMMING 127
4.1 Introduction 127
4.2 Definition of the subsystem and statement of the problem 127
4.3 Three methods of decomposition 131
4.3.1 The non feasible or goal coordination method 131
4.3.2 Model coordination or the feasible method 135
4.3.3 The mixed method 138
4.3.4 Comparison of the three methods 141
4.3.5 Extension to non linear coupling between the
subsystems 141
4.3.6 Economic interpretation 144
4.3.7 Examples 145
4.4 Convergence of coordination algorithms 155
4.4.1 Gradient coordination 155
4.4.1.1 Use of Lyapunov s method with continuous 155
time coordinator
4.4.1.2 Use of Lyapunov s method with optimisation 157
type coordination
4.4.2 Newton type coordination 158
4.4.3 Direct study of iterative decomposition
coordination methods 159
4.5 Extension to the case of inequality constraints 160
4.5.3 The feasible method 161
4.5.2 The non feasible method 161
4.6 Non separable problems . 164
4.6.1 Augmentation of the coordination vector 164
4.6.2 Introduction of pseudo variables 166
X
4.7 Applications 167
4.7.1 Stock building 167
4.7.2 Management of hydroelectric systems 173
4.7.2.1 Management strategies for production
of electricity 173
4.7.2.2 Short term management of hydro electric
thermal power systems 175
4.7.3 Solution of a distributed parameter problem
using a single processor and using a multi processor 185
4.7.3.1 The control of a distributed parameter system 185
4.7.3.2 Hierarchical solution using the feasible
method 189
4.7.3.3 Hierarchical solution using the multi¬
processor system 190
4.8 Conclusions 195
References for chapter 4 196
Problems for chapter 4 198
PART 2 : DYNAMIC OPTIMISATION AND CONTROL 199
Chapter 5 : DYNAMIC OPTIMISATION FOR LOW ORDER SYSTEMS 199
5.1 The dynamic optimisation problem 199
5.2 Variational techniques and the maximum principle 201
5.2.1 Necessary conditions of optimality 201
5.2.2 Boundary conditions 204
5.2.2.1 Problems with fixed terminal time 204
5.2.2.2 Problems with free terminal time 205
5.2.3 Examples ¦ 206
5.2.4 Linear quadratic problems 210
5.2.4.1 The linear regulator 210
5.2.4.2 Examples of L Q problems 212
5.2.4.3 The linear servomechanism problem 215
5.2.5 Singular solutions using the maximum principle 225
5.3 The discrete Maximum principle 230
5.3.1 Necessary conditions of optimality 230
5.3.2 Examples 234
5.3.3 Discrete linear quadratic problems 235
5.3.3.1 The regulator problem 235
5.3.3.2 The servomechanism problem 237
5.4 Dynamic programming and Hamilton Jacobi equation 241
5.4.1 Bellman s principle Hamilton Jacobi condition 241
5.4.2 Example 243
5.5 Conclusions 246
xi
References for chapter 5 246
Problems for chapter 5 247
Chapter 6 : HIERARCHICAL OPTIMISATION AND CONTROL FOR LINEAR SYSTEMS
WITH QUADRATIC COST FUNCTION 249
6.1 Introduction 249
6.2 The Goal coordination approach 251
6.2.1 Formulation 251
6.2.2 Comments 253
6.2.3 Example 1 255
6.3 Example 2 : Pearson s 12th order example 256
6.4 The three level method of Tamura 259
6.4.1 The Goal coordination method for discrete
dynamical systems 259
6.4.2 The modification of Tamura 260
6.4.3 Remarks 263
6.4.4 Example 263
6.5 The time delay algorithm of Tamura 264
6.6 Example : control of rush hour traffic 268
6.6.1 Model of an oversaturated traffic network 268
6.6.2 Cost function 270
6.6.3 An example 270
6.6.4 Simulation results 273
6.7 The interaction prediction approach 274
6.8 River pollution control 276
6.8.1 Simulation results 279
6.8.2 The six reach river problem 280
6.9 Avoiding singularities in the goal coordination method 281
6.10 Hierarchical Feedback control : motivation 288
6.11 The interaction prediction approach to decentralised control 288
6.11.1 Modification to give partial feedback control 290
6.11.2 Remarks 291
6.12 The closed loop controller 291
6.12.1 The regulator solution 292
6.12.2 Remarks 293
6.12.3 Example 293
6.13 Extension to the servomechanism case 295
6.14 Example : River pollution control 296
6.14.1 River pollution control models 296
6.14.2 The optimisation problem 298
6.14.3 Feedback control for a two reach river system 298
6.14.3.1 No delay model 298
6.14.3.2 Pure delay model 301
xvi
6.14.3.3 Distributed delay model 304
6.14.4 Control of the 3 reach distributed delay model 307
6.15 Example : Feedback control for power system 310
6.16 Open loop hierarchical optimisation by duality and
decomposition 314
6.16.1 Problem formulation 314
6.16.2 Open loop hierarchical optimisation structure 314
6.16.3 The algorithm 316
6.16.4 Remarks 317
6.17 A Multi level solution of the infinite stage regulator 317
6.18 Simulation example 318
6.19 Conclusions 321
References for chapter 6 322
Problems for chapter 6 324
Chapter 7 : DYNAMICAL OPTIMISATION FOR NON LINEAR SYSTEMS 329
7.1 Formulation of non—linear two point boundary value problems 329
7.2 The gradient method 330
7.2.1 The gradient method for parametric optimisation 330
7.2.2 The gradient method for functional optimisation 332
7.3 Quasilinearisation 345
7.3.1 Linearisation 346
7.3.2 Convergence 348
7.3.3 The case of the optimisation problem 349
7.3.4 The algorithm 350
7.3.5 Examples 353
7.4 The variation of extremals method 366
7.4.1 Determination of influence function matrices 369
7.4.2 The variation of extremals algorithm 371
7.5 Comparison of the three methods 375
7.6 The invariant imbedding method 377
7.7 Conclusions 380
References for chapter 7 381
Problems for chapter 7 382
Chapter 8 ; DYNAMIC OPTIMISATION FOR LARGE SCALE NON LINEAR SYSTEMS 385
8.1 The goal coordination method 385
8.2 The new prediction method of Hassan and Singh 390
8.3 Extension to the case of non linear non separable problems 401
8.4 The costate prediction method 406
xiii
8.5 The three level costate prediction method for continuous
dynamical systems 420
8.6 Hierarchical model following controller 424
8.7 Closed loop control for non linear systems 433
8.8 Conclusions 437
References for chapter 8 438
Problems for chapter 8 439
PART 3 : STOCHASTIC PROBLEMS
Chapter 9 : INTRODUCTION TO PROBABILITY THEORY AND STOCHASTIC PROCESSES 441
9.1 Introduction to Probability theory 441
9.1.1 Description of a random variable 443
9.1.2 Moment generating functions and characteristic
functions 445
9.1.3 Mathematical expectation, covariance, correlation,
independence 449
9.1.4 Conditional probability density functions and
conditional expectations 450
9.2 Gaussian random vectors 452
9.2.1 Linear transformation of Gaussian random
variables 453
9.2.2 Calculation of the conditional expectation 455
9.3 Stochastic processes 456
9.3.1 Description of a stochastic process 456
9.3.2 Gaussian stochastic processes 457
9.3.3 Stationarity 458
9.3.4 Markov processes 459
9.4 Dynamical systems and Gauss Markov processes 462
9.5 Continuous dynamical systems 467
9.6 Conclusions 472
References for chapter 9 473
Problems for chapter 9 474
Chapter 10 : STATE AND PARAMETER ESTIMATION 477
10.1 Elements of estimation theory 477
10.1.1 Principal properties of the estimate 477
10.1.2 Principal methods and obtaining estimates 478
10.2 Parameter estimation in linear static systems 480
10.3 Application of the least squares method to parameter
estimation for a dynamical model 483
ariv
10.4 Input output relationship for a noisy dynamical system 487
10.5 The generalised least squares method 489
10.6 The instrumental variable method 491
10.7 The Kalman Filter 493
10.7.1 Some useful properties of Gaussian random vectors 493
10.7.2 Discrete model 494
10.7.3 The optimal filter problem 495
10.8 Development of the filter equations 496
10.9 Continuous time estimation 506
10.10 Optimal stochastic control 510
10.10.1 The discrete time stochastic controller 510
10.10.2 Stochastic controller for continuous systems 524
10.11 Conclusions 524
References for chapter 10 525
Problems for chapter 10 526
Chapter 11 : ESTIMATION THEORY AND STOCHASTIC CONTROL FOR LARGE SCALE
SYSTEMS 529
11.1 The maximum a posteriori approach 529
11.2 The optimal filter of Pearson 533
11.3 The sub optimal filter of Shah 534
11.4 The continuous time S.P.A. Filter 537
11.5 The decentralised calculation structure for the optimal
Kalman filter 541
11.6 The algebraic structure of the New filter 543
11.7 The stochastic control problem using the New filter 556
11.8 The duality approach to optimal stochastic control of
L.Q.G. Problems 561
11.8.1 General considerations 561
11.8.2 The three level prediction principle controller
of Hassan et al. 562
11.9 Application to the 52nd order river pollution control problem 565
11.10 Conclusions 568
References for chapter 11 576
Problems for chapter 11 577
PART 4 : ROBUST DECENTRALISED CONTROL
Chapter 12 : ROBUST DECENTRALISED CONTROL 579
12.1 Introduction 579
12.2 A hierarchical structure for computing decentralised control 579
12.2.1 The three level calculation structure 581
12.2.2 Suboptimal bounds 584
12.2.3 Decentralised controller with a pre specified
degree of stability 586
12.2.4 The hierarchical computational structure to
compute decentralised control 592
12.2.5 Stability of the decentralised control system 595
12.3 The decentralised controller design 599
12.3.1 The general approach 599
12.3.2 Robust decentralised controller with a pre
specified degree of stability 614
12.3.3 Stability of the system on implementing the
decentralised controllers 617
12.4 Robust decentralised controller using a model follower 620
12.4.1 Problem formulation 620
12.4.2 Stability of the global system using the
decentralised controllers 624
12.5 Conclusions 627
References for chapter 12 639
Problems for chapter 12 640
AUTHOR INDEX 641
SUBJECT INDEX 643
|
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| id | DE-604.BV002297292 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T15:43:35Z |
| institution | BVB |
| isbn | 0080221505 |
| language | English |
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| record_format | marc |
| series2 | Pergamon international library of science, technology, engineering and social studies. |
| spelling | Systems: Decomposition, optimisation and control ed. by M. G. Singh ... Oxford Pergamon Press 1978 XV, 645 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Pergamon international library of science, technology, engineering and social studies. Commande, théorie de la ram Systèmes, analyse de ram Control theory System analysis Systemtheorie (DE-588)4058812-9 gnd rswk-swf Regelungstheorie (DE-588)4122327-5 gnd rswk-swf Optimierung (DE-588)4043664-0 gnd rswk-swf Kontrolltheorie (DE-588)4032317-1 gnd rswk-swf Optimierung (DE-588)4043664-0 s Kontrolltheorie (DE-588)4032317-1 s DE-604 Systemtheorie (DE-588)4058812-9 s Regelungstheorie (DE-588)4122327-5 s 1\p DE-604 Singh, Madan G. Sonstige oth HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001509875&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 | Systems: Decomposition, optimisation and control Commande, théorie de la ram Systèmes, analyse de ram Control theory System analysis Systemtheorie (DE-588)4058812-9 gnd Regelungstheorie (DE-588)4122327-5 gnd Optimierung (DE-588)4043664-0 gnd Kontrolltheorie (DE-588)4032317-1 gnd |
| subject_GND | (DE-588)4058812-9 (DE-588)4122327-5 (DE-588)4043664-0 (DE-588)4032317-1 |
| title | Systems: Decomposition, optimisation and control |
| title_auth | Systems: Decomposition, optimisation and control |
| title_exact_search | Systems: Decomposition, optimisation and control |
| title_full | Systems: Decomposition, optimisation and control ed. by M. G. Singh ... |
| title_fullStr | Systems: Decomposition, optimisation and control ed. by M. G. Singh ... |
| title_full_unstemmed | Systems: Decomposition, optimisation and control ed. by M. G. Singh ... |
| title_short | Systems: Decomposition, optimisation and control |
| title_sort | systems decomposition optimisation and control |
| topic | Commande, théorie de la ram Systèmes, analyse de ram Control theory System analysis Systemtheorie (DE-588)4058812-9 gnd Regelungstheorie (DE-588)4122327-5 gnd Optimierung (DE-588)4043664-0 gnd Kontrolltheorie (DE-588)4032317-1 gnd |
| topic_facet | Commande, théorie de la Systèmes, analyse de Control theory System analysis Systemtheorie Regelungstheorie Optimierung Kontrolltheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001509875&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT singhmadang systemsdecompositionoptimisationandcontrol |