Banks / Pritchard Control of Distributed Parameter Systems

Proceedings of the Second IFAC Symposium, Coventry, Great Britain, 28 June - 1 July 1977
1. Auflage 2014
ISBN: 978-1-4831-5112-0
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 554 Seiten, Web PDF

Control of Distributed Parameter Systems covers the proceedings of the Second IFAC Symposium, Coventry, held in Great Britain from June 28 to July 1, 1977. The book focuses on the methodologies, processes, and techniques in the control of distributed parameter systems, including boundary value control, digital transfer matrix, and differential equations. The selection first discusses the asymptotic methods in the optimal control of distributed systems; applications of distributed parameter control theory of a survey; and dual variational inequalities for external eigenvalue problems. The book also ponders on stochastic differential equations in Hilbert space and their application to delay systems and linear quadratic optimal control problem over an infinite time horizon for a class of distributed parameter systems. The manuscript investigates the semigroup approach to boundary value control and stability of nonlinear distributed parameter systems. Topics include boundary control action implemented through a dynamical system; classical boundary value controls; stability of nonlinear systems; and feedback control on the boundary. The text also focuses on the functional analysis interpretation of Lyapunov stability; method of multipliers for a class distributed parameter systems; and digital transfer matrix approach to distributed system simulation. The selection is a dependable source of data for readers interested in the control of distributed parameter systems.

Autoren/Hrsg.

Banks, S. P.

Pritchard, A. J.

Inhaltsverzeichnis

1;Front Cover;1
2;Control of Distributed Parameter Systems;4
3;Copyrigh Page;5
4;Table of Contents;8
5;Foreword;12
6;CHAPTER 1. ASYMPTOTIC METHODS IN THE OPTIMAL CONTROL OF DISTRIBUTED SYSTEMS;14
6.1;1. INTRODUCTION;14
6.2;2. PERTURBATION OF THE STATE EQUATION. THE CASE OF A "CONTINUOUS" COST FUNCTION;16
6.3;3. PERTURBATION OF THE STATE EQUATION. THE CASE WHERE THE COST FUNCTION IS NOT DEFINED ON THE LIMIT SPACE.;20
6.4;4. PERTURBATION OF THE COST FUNCTION;26
6.5;5. DEGENERACY OF THE COST FUNCTION (CHEAP CONTROL);28
6.6;6. PERTURBATIONS OF THE DOMAIN.;29
6.7;REFERENCES;33
7;CHAPTER 2. SOME RECENT APPLICATIONS OF DISTRIBUTED PARAMETER CONTROL THEORY A SURVEY;34
7.1;ABSTRACT;34
7.2;INTRODUCTION;34
7.3;BRIEF SUMMARY OF APPLIED DISTRIBUTED PARAMETER CONTROL THEORY;34
7.4;SOME REPORTED APPLICATIONS;35
7.5;CONCLUDING REMARKS;37
7.6;REFERENCES;37
8;CHAPTER 3. DUAL VARIATIONAL INEQUALITIES FOR EXTREMAL EIGENVALUE PROBLEMS;48
8.1;ABSTRACT;48
8.2;INTRODUCTION;48
8.3;2. STABILITY PROBLEMS FOR PERIODIC DIFFERENTIAL EQUATIONS;49
8.4;3. STRUCTURAL OPTIMIZATION PROBLEMS;51
8.5;4. NECESSARY AND SUFFICIENT OPTIMALITY CONDITIONS;52
8.6;5. DUAL EXTREMAL EIGENVALUE PROBLEMS;53
8.7;References;57
9;CHAPTER 4. STOCHASTIC DIFFERENTIAL EQUATIONS IN HILBERT SPACE AND THEIR APPLICATION TO DELAY SYSTEMS;58
9.1;ABSTRACT;58
9.2;INTRODUCTION;58
9.3;2. PRELIMINARIES;59
9.4;3. STOCHASTIC EVOLUTION EQUATIONS WITH STATE DEPENDENT NOISE ;60
9.5;4. STOCHASTIC LINEAR DELAY EQUATIONS WITH MARTINGALE NOISE;64
9.6;REFERENCES;67
10;CHAPTER 5. THE LINEAR QUADRATIC OPTIMAL CONTROL PROBLEM OVER AN INFINITE TIME HORIZON FOR A CLASS OF DISTRIBUTED PARAMETER SYSTEMS;70
10.1;ABSTRACT;70
10.2;1. INTRODUCTION;70
10.3;2. PRELIMINARIES AND PROBLEM FORMULATION;71
10.4;3. ASYMPTOTIC BEHAVIOUR AND L2-STABILITY;71
10.5;4. THE OPTIMAL CONTROL PROBLEM IN [0,-[;72
10.6;5. RELATIONSHIPS BETWEEN CONTROLLABILITY AND STABILIZABILITY;73
10.7;6. EXAMPLES;75
10.8;REFERENCES;76
11;CHAPTER 6. INITIAL-VALUE CONTROL OF THE KORTEWEG-DE VRIES EQUATION;80
11.1;ABSTRACT;80
11.2;INTRODUCTION;80
11.3;WELL-POSEDNESS OF THE INITIAL-VALUE PROBLEM;80
11.4;AN INITIAL-VALUE CONTROL PROBLEM;81
11.5;REFERENCES;84
12;CHAPTER 7. ON QUASIEQUILIBRIUM STATES AND RANGE DEGENERACY FOR LINEAR SEMIGROUP SYSTEMS;88
12.1;ABSTRACT;88
12.2;INTRODUCTION;88
12.3;BASIC DEFINITIONS;88
12.4;FUNDAMENTAL PROPERTIES OF QEQ AND DED;89
12.5;DUALITY BETWEEN QEQ AND DED;92
12.6;MORE ON FDE SYSTEMS;92
12.7;APPLICATION TO STABILIZATION PROBLEM;93
12.8;CONCLUDING REMARKS;96
12.9;ACKNOWLEDGEMENT;96
12.10;REFERENCES;96
13;CHAPTER 8. TIME-INVARIANCE OF THE REACHABLE SET FOR LINEAR CONTROL PROBLEMS;98
13.1;References;102
14;CHAPTER 9. SEMIGROUPS ON PRODUCT SPACES WITH APPLICATION TO INITIAL VALUE PROBLEMS WITH NON-LOCAL BOUNDARY CONDITIONS;104
14.1;ABSTRACT;104
14.2;1. INTRODUCTION;104
14.3;2. STATEMENT OF RESULTS;105
14.4;3. SOME SPECIAL CASES;106
14.5;4. PROOF OF THEOREM 2.1 (OUTLINE);106
14.6;5. APPLICATIONS;108
14.7;REFERENCES;111
15;CHAPTER 10. A SEMIGROUP APPROACH TO BOUNDARY VALUE CONTROL;112
15.1;1. INTRODUCTION;112
15.2;2. BOUNDARY CONTROL ACTION IMPLEMENTED THROUGH A DYNAMICAL SYSTEM. Examples;112
15.3;3. BOUNDARY CONTROL ACTION IMPLEMENTED THROUGH A DYNAMICAL SYSTEM , General model;113
15.4;4. DISCUSSION OF THE MODEL;116
15.5;5. FEEDBACK CONTROL ON THE BOUNDARY;117
15.6;6. SOME OPEN PROBLEMS;118
15.7;7. CLASSICAL BOUNDARY VALUE CONTROLS;118
15.8;REFERENCES;120
16;CHAPTER 11. STABILITY OF NONLINEAR DISTRIBUTED PARAMETER SYSTEMS;122
16.1;ABSTRACT;122
16.2;1. INTRODUCTION;122
16.3;2. SURVEY OF THE LITERATURE;122
16.4;3. EXISTENCE ..T UNIQUENESS OF SOLUTIONS;123
16.5;4. STABILITY OF LINEAR SYSTEMS;124
16.6;5. NONLINEAR SYSTEMS;126
16.7;6. FINAL REMARKS;131
16.8;7. REFERENCES;131
17;CHAPTER 12. STABILITY OF ABSTRACT EVOLUTION EQUATIONS;134
17.1;1 INTRODUCTION;134
17.2;2 PERTURBATIONS OF LINEAR SEMI-GROUPS;135
17.3;3 PERTURBATION THEOREMS FOR NON-LINEAR OPERATORS;141
17.4;References;145
18;CHAPTER 13. BIFURCATIONS TO DIVERGENCE AND FLUTTER IN FLOW-INDUCED OSCILLATIONS:an infinite dimensional analysis;146
18.1;ABSTRACT;146
18.2;1. INTRODUCTION;146
18.3;2. EXISTENCE, UNIQUENESS AND SMOOTHNESS;146
18.4;3. CENTRE MANIFOLD THEORY AND BIFURCATIONS;148
18.5;4. FINITE DIMENSIONAL APPROXIMATIONS AND CONVERGENCE;150
18.6;5. AN EXAMPLE BASED ON A TWO MODE MODEL OF PANEL FLUTTER;151
18.7;6. CONCLUSIONS;152
18.8;ACKNOWLEDGEMENTS;153
18.9;REFERENCES;153
19;CHAPTER 14. ON THE PATH INTEGRAL AND LYAPUNOV FUNCTIONAL FOR A CLASS OF DISTRIBUTED SYSTEMS;160
19.1;ABSTRACT;160
19.2;1. INTRODUCTION;160
19.3;2. STATEMENT OF PROBLEMS AND PATH INTEGRALS;160
19.4;3. RESULTS AND LYAPUNOV FUNCTIONALS;162
19.5;4. APPLICATIONS;164
19.6;5. CONCLUSIONS;167
19.7;Acknowledgment;167
19.8;APPENDIX A;167
19.9;APPENDIX B;167
19.10;References;169
20;CHAPTER 15. THE FUNCTIONAL ANALYSIS INTERPRETATION OF LYAPUNOV STABILITY;170
20.1;ABSTRACT;170
20.2;INTRODUCTION;170
20.3;DYNAMIC SYSTEM;170
20.4;DEFINITIONS OF STABILITY;171
20.5;GENERAL IDEA OF THE LYAPUNOV METHOD;172
20.6;INTERPRETATION OF CLASSICAL METHODS;173
20.7;VECTOR LYAPUNOV PUNCTIONALS;174
20.8;CONCLUSIONS;174
20.9;REFERENCES;175
21;CHAPTER 16. STABILITY CONDITIONS AND DESIGN OF CONTROL USING LIAPUNOV-ZUBOV FUNCTIONALS;176
21.1;ABSTRACT;176
21.2;INTRODUCTION;176
21.3;THEOREMS ON THE STABILITY;177
21.4;INTEGRAL FORM OF THE LIAPUNOW-ZUBOV FUUCT10NALS;182
21.5;CONTROL OF PIPE LINES;182
21.6;REFERENCES;184
22;CHAPTER 17. ON THE METHOD OF MULTIPLIERS FOR A CLASS OF DISTRIBUTED PARAMETER SYSTEMS;186
22.1;ABSTRACT;186
22.2;1. INTRODUCTION;186
22.3;2. NOTATIONS AND ASSUMPTIONS;186
22.4;3. BOUNDARY CONTROL PROBLEMS;187
22.5;4. DISTRIBUTED CONTROL PROBLEMS;190
22.6;5. CONCLUDING REMARKS;193
22.7;REFERENCES;193
23;CHAPTER 18. A DIGITAL TRANSFER MATRIX APPROACH TO DISTRIBUTED SYSTEM SIMULATION;194
23.1;ABSTRACT;194
23.2;INTRODUCTION;194
23.3;DERIVATION OF THE ALGORITHMS;195
23.4;AN EXAMPLE: HEAT TRANSFER IN MULTI-LAYER SLABS;201
23.5;CONCLUSION;204
23.6;ACKNOWLEDGEMENTS;204
23.7;REFERENCES;204
24;CHAPTER 19. ERRORS IN THE FINITE DIFFERENCE SOLUTION OF HYPERBOLIC PARTIAL DIFFERENTIAL EQUATIONS;206
24.1;INTRODUCTION;206
24.2;SYSTEM EQUATIONS;206
24.3;SIMULTANEOUS ORDINARY DIFFERENTIAL EQUATIONS;207
24.4;ERROR ANALYSIS;207
24.5;FINITE DIFFERENCE GRID SPACING;208
24.6;METHOD OF CHARACTERISTICS;209
24.7;EXAMPLE;209
24.8;CONCLUSION;210
24.9;REFERENCES;211
24.10;APPENDIX I;211
24.11;APPENDIX 2;211
25;CHAPTER 20. DESIGN OF DISTRIBUTED-PARAMETER OPTIMALCONTROLLERS AND FILTERS VIA WALSH-GALERKIN EXPANSIONS;214
25.1;ABSTRACT;214
25.2;INTRODUCTION;214
25.3;2. THE BASIC WALSH-GALERKIN EXPANSION TECHNIQUE;215
25.4;3. THE DISTRIBUTED-PARAMETER OPTIMAL CONTROLLER AND FILTER DESIGN PROBLEMS;218
25.5;4. WALSH-GALERKIN IMPLEMENTATION OF THE OPTIMAL CONTROLLER;220
25.6;5. IMPROVED WALSH-RITZ-GALERKIN EXPANSION TECHNIQUE;222
25.7;6. WALSH-GALERKIN SOLUTION OF DISTRIBUTED-PARAMETER VARIATIONAL PROBLEMS;223
25.8;7. EXAMPLES;226
25.9;8. CONCLUSION;227
25.10;REFERENCES;227
26;CHAPTER 21. OBSERVERS FOR BILINEAR DISTRIBUTED PARAMETER PROCESSES;232
26.1;ABSTRACT;232
26.2;1. INTRODUCTION;232
26.3;2. BILINEAR DISTRIBUTED PARAMETER SYSTEM - HEAT EXCHANGE PROCESS;233
26.4;3. BILINEAR OBSERVERS;235
26.5;4. LUMPED PARAMETER APPROXIMATION BY USING THE METHOD OF WEIGHTED RESIDUALS (MWR);237
26.6;5. EXPERIMENTAL INVESTIGATION;238
26.7;6. CONCLUSION;241
26.8;REFERENCES;241
27;CHAPTER 22. INITIAL STATE DETERMINATION FOR DISTRIBUTED PARAMETER SYSTEMS WITH DISCRETE-TIME MEASUREMENT DATA;244
27.1;ABSTRACT;244
27.2;INTRODUCTION;244
27.3;STATEMENT OF THE PROBLEM;244
27.4;N-STEP OBSERVABILITY AND N-STEP OUTPUT CONTROLLABILITY WITH RESPECT TO THE INITIAL STATE;245
27.5;MINIMIZATION OF J(n);246
27.6;DUAL PROBLEM;246
27.7;A WELL-POSED APPROXIMATION METHOD;246
27.8;THE SYSTEM WITH POINTWISE OBSERVATION;248
27.9;CONCLUSIONS;249
27.10;NUMERICAL RESULTS;249
27.11;REFERENCES;249
28;CHAPTER 23. PARAMETER AND STATE ESTIMATION FOR A DIFFUSION PROCESS;252
28.1;REFERENCES;258
29;CHAPTER 24. DIFFERENTIAL STATE SPACE DESCRIPTIONS OF NONLINEAR TIME VARIANT HEREDITARY DIFFERENTIAL SYSTEMS;260
29.1;ABSTRACT;260
29.2;.. INTRODUCTION;260
29.3;2. THE PROBLEM OF DIFFERENTIAL STATE SPACE DESCRIPTION;261
29.4;3. DIFFERENTIABILITY OF THE SEGMENT FUNCTION t —>xt ;263
29.5;4. SOLUTIONS OF z(t) = A z(t);268
29.6;5. CONCLUSIONS;270
29.7;REFERENCES;272
30;CHAPTER 25. F- REDUCTION OF THE OPERATOR RICCATI EQUATIONS FOR HEREDITARY DIFFERENTIAL SYSTEMS;274
30.1;1. INTRODUCTION;274
30.2;2. LINEAR AUTONOMOUS HDS;275
30.3;3. THE LINEAR QUADRATIC OPTIMAL CONTROL PROBLEM;277
30.4;REFERENCES;282
31;CHAPTER 26. OPTIMAL OUTPUT-FEEDBACK CONTROLLERS FOR LINEAR TIME-DELAY SYSTEMS;286
31.1;ABSTRACT;286
31.2;INTRODUCTION;286
31.3;PROBLEM FORMULATION;287
31.4;MAIN RESULT;288
31.5;CONCLUSION;289
31.6;REFERENCES;290
32;CHAPTER 28. FINITE DIFFERENCE APPROXIMATION OF STATE AND CONTROL CONSTRAINED OPTIMAL CONTROL PROBLEM FOR SYSTEM WITH DELAY;292
32.1;ABSTRACT;292
32.2;NOTATIONS;292
32.3;CONTINUOUS OPTIMAL CONTROL PROBLEM STATEMENT;292
32.4;LAGRANGE FORMALISM;293
32.5;DISCRETE OPTIMAL CONTROL PROBLEM STATEMENT;294
32.6;ESTIMATION OF THE RATE OF CONVERGENCE;296
32.7;REFERENCES;297
33;CHAPTER 29. NECESSARY AND SUFFICIENT CONDITIONS FOR DESIGNING OPTIMAL FEEDBACK CONTROLLERS FOR LINEAR DYNAMICAL SYSTEMS WITH MULTIPLE TIME DELAYS;298
33.1;ABSTRACT;298
33.2;I. INTRODUCTION;298
33.3;II. CANONICAL DECOMPOSITION;299
33.4;III. THE LINEAR-QUADRATIC REGULATOR THEORY FOR NON-DELAYED SYSTEMS;301
33.5;IV. THE LINEAR-QUADRATIC REGULATOR THEORY FOR DELAYED SYSTEMS;301
33.6;V. EXAMPLE;303
33.7;IV, CONCLUSION;303
33.8;ACKNOWLEDGMENTS;303
33.9;REFERENCES;303
34;CHAPTER 30. ON GOODNESS-OF-FIT STRUCTURE OF SOME DETERMINISTIC AND STOCHASTIC MODELS FOR EXPANDING ECONOMIES;306
34.1;ABSTRACT;306
34.2;1. INTRODUCTION;306
34.3;2. THE VON NEUMANN MODELS AND THEIR GENERALIZATIONS;307
34.4;3. TESTING STATISTICAL STRUCTURAL VALIDITY OF STOCHASTIC ECONOMIC MODELS;312
34.5;ACKNOWLEDGEMENT;319
34.6;REFERENCES;319
35;CHAPTER 31. ADAPTIVE OPEN LOOP CONTROL FOR A CLASS OF DISTRIBUTED PARAMETER SYSTEMS;322
35.1;ABSTRACT;322
35.2;SITUATION OF THE PROBLEM;322
35.3;METHODS OF SOLUTION;323
35.4;FORMULATION OF THE SOLUTION;324
35.5;SIMULATION - EXAMPLE;326
35.6;RESULTS;328
35.7;REFERENCES;330
36;CHAPTER 32. ON THE DISCRETE-TIME QUADRATIC OPTIMUM CONTROL PROBLEM IN REFLEXIVE BANACH SPACE;332
36.1;ABSTRACT;332
36.2;1. INTRODUCTION;332
36.3;2. NOTATION AND PRELIMINARIES;333
36.4;3. PROBLEM FORMULATION AND BASIC SOLUTION;334
36.5;4. THE OPTIMUM CONTROL LAW;335
36.6;5. OPTIMUM CONTROL PROBLEM ON INFINITE TIME SET;336
36.7;6. THE CONVERGENCE PROBLEM;337
36.8;CONCLUSIONS;340
36.9;ACKNOWLEDGEMENT;340
36.10;REFERENCES;340
37;CHAPTER 33. SIMPLIFIED OPTIMUM CONTROL OF DISTRIBUTED PARAMETER SYSTEMS;342
37.1;ABSTRACT;342
37.2;INTRODUCTION;342
37.3;OPEN-LOOP OPTIMAL CONTROL;343
37.4;CLOSED-LOOP CONTROL;343
37.5;NUMERICAL EXAMPLE;345
37.6;CONCLUSIONS;348
37.7;REFERENCES;348
38;CHAPTER 34. A STOCHASTIC DIFFERENTIAL GAME AS CONTROL PROBLEM WITH INFINITE DIMENSIONAL STATE SPACE;350
38.1;ABSTRACT;350
38.2;1 INTRODUCTION;350
38.3;2 GAUSS MEASURE AND WHITE NOISE;351
38.4;3 LINEAR-QUADRATIC GAME: LUMPED PARAMETER CASE;352
38.5;4 LINEAR-QUADRATIC GAME: DISTRIBUTED PARAMETER CASE;356
38.6;5 CONCLUSION;358
39;CHAPTER 35. FILTERING AND CONTROL OF DISTRIBUTED PARAMETER SYSTEMS WITH POINT OBSERVATIONS AND INPUTS;360
39.1;ABSTRACT;360
39.2;INTRODUCTION;360
39.3;1. THE MODEL AND OPTIMAL LOCATION PROBLEM;361
39.4;2. AN EXAMPLE OF A HEAT EQUATION;363
39.5;3. NUMERICAL RESULTS;364
39.6;4. CONCLUSION;367
39.7;REFERENCES;367
40;CHAPTER 36. THE SOLUTION OF SOME IDENTIFICATION PROBLEMS OF BIOMEDICAL SYSTEMS;372
40.1;ABSTRACT;372
40.2;INTRODUCTION;372
40.3;THE KINDS OF PROBLEMS;373
40.4;MATHEMATICAL FORMULATION OF THE PROBLEM;373
40.5;DESCRIPTION OF THE METHOD;374
40.6;ITERATIVE PROCESS;376
40.7;ERRORS;376
40.8;CONCLUSION;378
40.9;KEEERENOE;378
41;CHAPTER 37. GEOSTATISTICAL TECHNIQUES IN DISTRIBUTED PARAMETER SYSTEM ESTIMATION PROBLEMS;380
41.1;1 - INTRODUCTION;380
41.2;2 - GEOSTATISTICAL MODELS;381
41.3;3 - APPLICATION OF THE MODEL TO THE ESTIMATION OF A LINEAR FUNCTION OF A ReV;385
41.4;4 - USING I.R.F.k TO ESTIMATE LINEAR FUNCTIONS OF A NON STATIONARY RF;387
41.5;CONCLUSION;390
41.6;ACKNOWLEDGEMENTS;390
41.7;REFERENCES;390
42;CHAPTER 38. IDENTIFIABILITY OF INTERNAL AND BOUNDARY PARAMETERS IN SYSTEMS OF PARABOLIC TYPE;394
42.1;ABSTRACT;394
42.2;1. Introduction;394
42.3;2 . Statement of the Identiflability Problem;395
42.4;3 . Distributed Measurement;396
42.5;4 . Pointwise Measurement;401
42.6;5. Conclusion;404
42.7;Acknowledgement;404
42.8;REFERENCES;405
43;CHAPTER 39. FREQUENCY DOMAIN SIMULATION AND IDENTIFICATION OF DISTRIBUTED SYSTEMS;406
43.1;ABSTRACT;406
43.2;INTRODUCTION;406
43.3;THEORY;407
43.4;EXAMPLE;409
43.5;REFERENCES;412
44;CHAPTER 40. AN ATTEMPT TO IDENTIFY THE VISUAL AND MANUAL PHENOMENA FOR A HUMAN OPERATOR SUBMITTED TO VESTIBULAR STIMULATIONS (PITCH MOTION) DURINGVISUAL DETECTION TASKS;414
44.1;INTRODUCTION;414
44.2;I - STATEMENT OF THE PROBLEM;414
44.3;II - EXPERIMENTAL CONTROL SLT UP AND CHARACTERIZATION OF INPUT, OUTPUT AND PERTURBATION VARIABLES;415
44.4;Ill - PREVIOUS RESULTS (5.6);416
44.5;IV- VISUAL TASK PARAMETERS IDENTIFICATION;418
44.6;V - SYNTHESIS OF THE RESULT. MODEL FOR THE HUMAN OPERATOR BEHAVIOR IN A MOVING MECHANICAL WORKING STATION;423
44.7;CONCLUSION;425
44.8;BIBLIOGRAPHY;425
45;CHAPTER 41. OPTIMAL CONTROL OF CHEMICAL PLANTS WITH STAGES SUBJECT TO RANDOM BREAKDOWNS;426
45.1;ABSTRACT;426
45.2;INTRODUCTION;426
45.3;MARKOV JUMP DISTURBANCES AND MARKOV DECISION PROCESSES;426
45.4;A BALANCING PROBLEM IN THE PRODUCTION OF VINYL CHLORIDE;428
45.5;A MARKOV CHAIN APPROXIMATION;430
45.6;DISCUSSION;433
45.7;REFERENCES;434
45.8;APPENDIX;434
46;CHAPTER 42. MWR APPROXIMATION AND MODAL CONTROL OF PARALLEL- AND COUNTER-FLOW HEAT EXCHANGERS;436
46.1;ABSTRACT;436
46.2;1. INTRODUCTION;436
46.3;2. MWR APPROXIMATE SYSTEMS;437
46.4;3. MODAL CONTROL OF THE HEAT EXCHANGERS;441
46.5;4. CONCLUSIONS;447
46.6;NOMENCLATURE;447
46.7;REFERENCES;447
47;CHAPTER 43. CONTROL OF A DISTRIBUTED PARAMETER SYSTEM USING VECTOR PERFORMANCE INDEX;450
47.1;ABSTRACT;450
47.2;INTRODUCTION;450
47.3;THE STEAM GENERATOR SYSTEM;451
47.4;PARAMETER OPTIMIZATION VIA VECTOR PERFORMANCE INDEX;457
47.5;NUMERICAL RESULTS - SASM;458
47.6;NONLINEAR STEAM GENERATOR SYSTEM PERFORMANCE;460
47.7;DISCUSSION AND CONCLUSIONS;461
47.8;REFERENCES;461
47.9;ACKNOWLEDGEMENT;462
48;CHAPTER 44. THE REAL TIME APPLICATION OF DISTRIBUTED PARAMETER STATE ESTIMATION THEORY TO A TWO DIMENSIONAL HEATED INGOT;464
48.1;ABSTRACT;464
48.2;INTRODUCTION;464
48.3;THE EXPERIMENTAL PROCESS;464
48.4;THE STATE ESTIMATOR;471
48.5;EXPERIMENTAL RESULTS;475
48.6;CONCLUSIONS;478
48.7;ACKNOWLEDGEMENTS;478
48.8;NOMENCLATURE;478
48.9;REFERENCES;479
49;CHAPTER 45. STABILITY OF COUNTERCURRENTLY COOLED FIXED BED REACTORS;482
49.1;ABSTRACT;482
49.2;INTRODUCTION;482
49.3;MOBEL CONSIDERATIONS;482
49.4;CONCLUSIONS;488
49.5;NOTATION;488
49.6;REFERENCES;489
50;CHAPTER 46. A REDUCED MODEL FOR OPTIMAL CONTROL OF A GAS DISTRIBUTION NETWORK;492
50.1;ABSTRACT;492
50.2;INTRODUCTION;492
50.3;THE FLOW CONTROL PROBLEM;492
50.4;FORMULATION OF MODEL;493
50.5;FORMULATION OF MODEL;493
50.6;MODEL REDUCTION;494
50.7;EVALUATION OF REDUCED MODELS;496
50.8;SYNTHESIS OF AN OPTIMAL CONTROL ALGORITHM;497
50.9;NOTATION;499
50.10;SUBSCRIPTS;500
50.11;BREAK LETTERS;500
50.12;REFERENCES;500
50.13;ACKNOWLEDGEMENT;500
51;CHAPTER 47. PHENOMENOLOGICAL INVESTIGATION OF A DISTRIBUTED PARAMETER MODEL FOR COORDINATING THE MECHANICAL ACTIVITY OF THE MAMMALIAN GUT;506
51.1;ABSTRACT;506
51.2;1. INTRODUCTION;506
51.3;2. MODELLING THEORY;507
51.4;3. SIMULATION RESULTS;516
51.5;4. CONCLUSIONS;521
51.6;5. ACKNOWLEDGEMENTS;521
51.7;6. REFERENCES;521
52;CHAPTER 48. OPTIMUM DESIGN OF DISTRIBUTED MASS AND STIFFNESS STRUCTURAL SYSTEMS UNDER CONSTRAINTS;524
52.1;ABSTRACT;524
52.2;INTRODUCTION;524
52.3;ANALYSIS;526
52.4;RESULTS;535
52.5;DISCUSSION;537
52.6;REFERENCES;538
53;CHAPTER 49. APPLICATIONS OF EXTENDED OPERATORS TO DIFFUSIVE SYSTEMS;540
53.1;ABSTRACT;540
53.2;1. INTRODUCTION;540
53.3;2. DERIVATION OF THE EXTENDED OPERATOR: AN EXAMPLE;541
53.4;3. EXTENDED OPERATOR TABLE FOR ID DIFFUSION EQUATION;541
53.5;5. HEAT DISTRIBUTION IN A COMPOSITE SLAB;542
53.6;6. FOURIER APPROXIMATIONS TO PERIOD;543
53.7;CONCLUSION;544
53.8;APPENDIX - DERIVATION OF THE EXTENDED OPERATOR;545
53.9;REFERENCES;545
54;LIST OF PARTICIPANTS;552
55;AUTHOR INDEX;554