Isidori Nonlinear Control Systems Design 1989

Selected Papers from the IFAC Symposium, Capri, Italy, 14-16 June 1989
1. Auflage 2014
ISBN: 978-1-4832-9892-4
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 421 Seiten, Web PDF

Reihe: IFAC Symposia Series

In the last two decades, the development of specific methodologies for the control of systems described by nonlinear mathematical models has attracted an ever increasing interest. New breakthroughs have occurred which have aided the design of nonlinear control systems. However there are still limitations which must be understood, some of which were addressed at the IFAC Symposium in Capri. The emphasis was on the methodological developments, although a number of the papers were concerned with the presentation of applications of nonlinear design philosophies to actual control problems in chemical, electrical and mechanical engineering.

Autoren/Hrsg.

Isidori, A.

Inhaltsverzeichnis

1;Front Cover;1
2;Nonlinear Control Systems Design ;4
3;Copyright Page
;5
4;Table Of Contents
;10
5;Ifac Symposium On Nonlinear Control Systems Design
;6
6;Preface
;8
7;CHAPTER 1. COMPUTER-AIDED DESIGN OF NONLINEAR OBSERVERS;16
7.1;INTRODUCTION;16
7.2;NONLINEAR OBSERVABILITY PROBLEM;16
7.3;EXTENDED LUENBERGER OBSERVER;17
7.4;PROGRAM FOR THE COMPUTER-AIDED OBSERVER DESIGN;18
7.5;EXAMPLE OF AN OBSERVER DESIGN;18
7.6;CONCLUSIONS;19
7.7;REFERENCES;19
8;CHAPTER 2. SHOULD THE THEORIES FOR CONTINUOUSTIME AND DISCRETE-TIME LINEAR AND NONLINEAR SYSTEMS REALLY LOOK ALIKE?;22
8.1;I. INTRODUCTION;22
8.2;II. DIFFERENCE ALGEBRA AND DISCRETE-TIME SYSTEMS;22
8.3;III. REALIZATON(5);23
8.4;IV. SOME EXAMPLES OF THE RELATONSHIP BETWEEN DISCRETE-TIME AND CONTIUOUS-TIME SYSTEMS;24
8.5;V. FEEDBACK LINEARIZATON;25
8.6;VI. CONCLUSION;26
8.7;REFERENCES;26
9;CHAPTER 3. DIFFERENTIAL ALGEBRA AND CONTROLLABILITY;28
9.1;Introduction;28
9.2;Linear case;28
9.3;Definition;28
9.4;Nonlinear case;28
9.5;.. Haddak;29
9.6;DIFFERENTIAL ALGEBRAIC APPROACH OF CONTROLLABILITY;30
9.7;Conclusion
;31
9.8;REFERENCES
;31
10;CHAPTER 4. PRIME DIFFERENTIAL IDEALS IN NONLINEAR RATIONAL CONTROL SYSTEMS;32
10.1;INTRODUCTION;32
10.2;RATONAL CONTROL SYSTEMS;32
10.3;APPLICATION TO THE DIFFERENTIAL OUTPUT RANK OF A NONLINEAR SYSTEM;34
10.4;CONCLUSION;36
10.5;REFERENCES;36
11;CHAPTER 5. CONTROLLABILITY OF BILINEAR SYSTEMS—A SURVEY AND SOME NEW RESULTS;38
11.1;INTRODUCTION;38
11.2;BRIEF SURVEY ON CONTROLLABILITY OF BILINEAR SYSTEMS;38
11.3;CONTROLLABILITY OF NONLINEAR SYSTEMS;39
11.4;STRICTLY BILINEAR SYSTEMS;39
11.5;HOMOGENEOUS-IN-THE-STATE BILINEAR SYSTEMS;39
11.6;TWO-DIMENSIONAL HOMOGENEOUS-IN-THE-STATE BILINEAR SYSTEMS;40
11.7;THREE-DIMENSIONAL HOMOGENEOUS-IN-THE-STATE BILINEAR SYSTEMS;40
11.8;CONCLUSIONS;41
11.9;ACKNOWLEDGMENT;41
11.10;REFERENCES;41
11.11;APPENDIX;42
12;CHAPTER 6. CONTROLLABILITY OF BILINEAR SYSTEMS—A SURVEY AND SOME NEW RESULTS;38
12.1;INTRODUCTION;38
12.2;BRIEF SURVEY ON CONTROLLABILITY OF BILINEAR SYSTEMS;38
12.3;CONTROLLABILITY OF NONLINEAR SYSTEMS;39
12.4;STRICTLY BILINEAR SYSTEMS;39
12.5;HOMOGENEOUS-IN-THE-STATE BILINEAR SYSTEMS;39
12.6;TWO-DIMENSIONAL HOMOGENEOUS-IN-THE-STATE BILINEAR SYSTEMS;40
12.7;THREE-DIMENSIONAL HOMOGENEOUS-IN-THE-STATE BILINEAR SYSTEMS;40
12.8;CONCLUSIONS;41
12.9;ACKNOWLEDGMENT;41
12.10;REFERENCES;41
12.11;APPENDIX;42
13;CHAPTER 7. DIFFERENTIAL ALGEBRA AND PARTIAL DIFFERENTIAL CONTROL THEORY;44
13.1;INTRODUCTION;44
13.2;A) DIFFERENTIAL GEOMETRY
;45
13.3;B) DIFFERENTIAL ALGEBRA:;45
13.4;CONCLUSION;47
13.5;REFERENCES;47
14;CHAPTER 8. CANONICAL FORMS FOR NONLINEAR SYSTEMS;48
14.1;1. INTRODUCTION;48
14.2;2. CONTROLLABILITY FORMS;49
14.3;3. CONTROLLER FORMS;50
14.4;4. OBSERVABILITY FORMS;50
14.5;5. OBSERVER FORMS;51
14.6;6. CONCLUSION;52
14.7;7. REFERENCES;53
15;CHAPTER 9. NEW SUFFICIENT CONDITIONS FOR DYNAMIC FEEDBACK LINEARIZATION;54
15.1;Abstract;54
15.2;1 INTRODUCTION;54
15.3;2 PRELIMINARIES;55
15.4;3 MAIN RESULT;55
15.5;4 EXAMPLES;57
15.6;5 CONCLUDING REMARKS;59
15.7;References;59
16;CHAPTER 10. ON THE STRUCTURE ALGORITHM, DEGENERATE CONTROLLED INVARIANT DISTRIBUTIONS AND THE BLOCK DECOUPLING PROBLEM;62
16.1;INTRODUCTION;62
16.2;THE STRUCTURE ALGORITHM OF HIRSCHORN(1979)
;62
16.3;THE STATIC STATE FEEDBACK BLOCK DECOUPLING PROBLEM;63
16.4;THE DYNAMIC BLOCK DECOUPLING PROBLEM;64
16.5;REFERENCES;66
17;CHAPTER 11. NONLINEAR MODEL MATCHING WITH ANAPPLICATION TO HAMILTONIAN SYSTEMS;68
17.1;1. INTRODUCTION;68
17.2;2. THE MODEL MATCHING PROBLEM;68
17.3;3. MODEL MATCHING WITH PRESCRIBED TRACKING ERROR;70
17.4;4. APPLICATION TO HAMILTONIAN SYSTEMS;70
17.5;
5. CONCLUSIONS;72
17.6;ACKNOWLEDGMENTS;73
17.7;REFERENCES;73
18;CHAPTER 12. NONLINEAR MODEL MATCHING WITH AN APPLICATION TO HAMILTONIAN SYSTEMS;68
18.1;1. INTRODUCTION;68
18.2;2. THE MODEL MATCHING PROBLEM;68
18.3;3. MODEL MATCHING WITH PRESCRIBED TRACKING ERROR;70
18.4;4. APPLICATION TO HAMILTONIAN SYSTEMS;70
18.5;5. CONCLUSIONS;72
18.6;ACKNOWLEDGMENTS;73
18.7;REFERENCES;73
19;CHAPTER 13. NONLINEAR MODEL MATCHING WITH AN APPLICATION TO HAMILTONIAN SYSTEMS;68
19.1;1. INTRODUCTION;68
19.2;2. THE MODEL MATCHING PROBLEM;68
19.3;3. MODEL MATCHING WITH PRESCRIBED TRACKING ERROR;70
19.4;4. APPLICATION TO HAMILTONIAN SYSTEMS;70
19.5;5. CONCLUSIONS;72
19.6;ACKNOWLEDGMENTS;73
19.7;REFERENCES;73
20;CHAPTER 14. VIRTUAL DECOMPOSITION AND TIME SCALE DECOUPLING CONTROL OF NONLINEAR SYSTEMS;74
20.1;INTRODUCTION;74
20.2;VIRTUAL DECOMPOSITION TO FULL-CONTROLLED SUBSYSTEMS ;74
20.3;FULL-CONTROLLED SYSTEMS;75
20.4;TIME SCALE DECOUPLING CONTROL;77
20.5;
CONCLUSION;78
20.6;ACKNOWLEDGMENT;78
20.7;
REFERENCES;78
21;CHAPTER 15. TRAJECTORY EQUIVALENCE AND WEAKLY INVARIANT DISTRIBUTIONS OF NONLINEAR SYSTEMS;80
21.1;INTRODUCTION;80
21.2;TIME SCALE TRANSFORMATION;80
21.3;TRAJECTORY EQUIVALENCE;81
21.4;WEAKLY INVARIANT DISTRIBUTION;82
21.5;CONTROLLABILITY DECOMPOSITION;83
21.6;CONCLUSION;84
21.7;REFERENCES;85
22;CHAPTER 16. ON THE STRUCTURE OF SMALL-TIME REACHABLE SETS FOR MULTI-INPUT NONLINEAR SYSTEMS IN LOW DIMENSIONS;86
22.1;INTRODUCTION;86
22.2;THE STRUCTURE OF THE SMALL-TIMEREACHABLE SET FOR A 4-DIMENSIONALSYSTEM WITH 2 CONTROLS;87
22.3;CONCLUSIONS;91
22.4;REFERENCES;91
23;CHAPTER 17. STRUCTURAL PROPERTIES OF REALIZATIONS OF EXTERNAL DIFFERENTIAL SYSTEMS;92
23.1;1. INTRODUCTION;92
23.2;3. (STRONG) ACCESSIBILITY AND UNIQUENESS OF MINIMAL REALIZATIONS;95
23.3;2. REALIZATION OF EXTERNAL DIFFERENTIAL SYSTEMS;92
23.4;4. A CONTROLLER CANONICAL FORM;96
23.5;4. CONCLUSION;96
23.6;REFERENCES;96
24;CHAPTER 18. ON THE USE OF STABLE DISTRIBUTIONS IN DESIGN PROBLEMS;98
24.1;1. INTRODUCTION;98
24.2;2. THE CONSTRUCTION OF STABLE DISTRIBUTIONS;98
24.3;3. THE LOCAL DISTURBANCE DECOUPLING PROBLEM WITH STABILITY;101
24.4;4. THE LOCAL NONINTERACTING CONTROL PROBLEM WITH STABILITY;102
24.5;5. CONCLUSIONS;102
24.6;ACKNOWLEDGEMENT;103
24.7;LITERATURE;103
25;CHAPTER 18. TARGET-DIRECTED CONTROL OF NONLINEAR SYSTEMS;104
25.1;1. INTRODUCTION;104
25.2;2. MATHEMATICAL PROGRAMMING BACKGROUND;104
25.3;3. CONTROL OF A NOMINAL PLANT;106
25.4;4 . FEEDBACK CONTROL OF A NON-NOMINAL PLANT;107
25.5;5. ILLUSTRATIVE EXAMPLE;108
25.6;REFERENCES;109
26;CHAPTER 19. ON THE CONTROLLABILITY OF NONLINEAR DISCRETE-TIME SYSTEMS;110
26.1;1-INTRODUCTION
;110
26.2;2-MAIN. RESULTS
;110
26.3;3 . E
XEMPLES;111
26.4;REFERENCES;111
27;CHAPTER 20. NONLINEAR DECOUPLING IN DISCRETE TIME;114
27.1;1. INTRODUCTION;114
27.2;2. PRELIMINARIES;114
27.3;3. STATE FREE INVERTIBILITY AND INVARIANT FOLIATIONS;115
27.4;4. INPUT-OUTPUT DECOUPLING VIA STATIC STATE FEEDBACK;117
27.5;5. INPUT-OUTPUT DECOUPLING VIA DYNAMIC STATE FEEDBACK;118
27.6;REFERENCES;120
27.7;APPENDIX THE INVERSE OF A SYSTEM OF FUNCTIONS;121
28;CHAPTER 21. RECURSIVE IDENTIFICATION ALGORITHMSAS NONLINEAR SYSTEMS: PARAMETER IDENTIFIABILITY AND CONTROLLABILITY;122
28.1;1.
INTRODUCTION;122
28.2;2. Assumptions and Definitions;123
28.3;3.Controllability of the Nonlinear System;123
28.4;4.CONTROLLABILITY OF THE ALGOR
ITHM;124
28.5;5. PARAMETER IDENTIFIABILITY;125
28.6;6.SOME
EXAMPLES;126
28.7;7. CONCLUDING REMARKS;126
28.8;R
EFEENCES;127
29;CHAPTER 22. NICELY NONLINEAR MODELLING: A DF APPROACH WITH APPLICATION TO "LINEARIZED" PROCESS CONTROL;128
29.1;1. INTRODUCTION;128
29.2;2. A CLASS OF NICELY NONLINEAR MODELS;129
29.3;4. BINARY DISTILLATION COLUMN: A SIMULATION STUDY;132
29.4;5. CONCLUDING REMARKS;133
29.5;ACKNOWLEDGMENT;133
29.6;REFERENCES;133
30;CHAPTER 23. NONLINEAR PREDICTIVE CONTROL BY INVERSION;134
30.1;INTRODUCTION;134
30.2;IHE TECHNIQUE DESCRIPTIOI;134
30.3;SOME REMARKS ON INVERSION;135
30.4;EXAMPLES;135
30.5;CONCLUSION;138
30.6;ACKNOWLEDGEMENTS;139
30.7;REFERENCES;139
31;CHAPTER 24. A VOLTERRA METHOD FOR NONLINEAR CONTROL DESIGN;140
31.1;INTRODUCTION;140
31.2;PROBLEM FORMULATION;140
31.3;VOLTERRA KERNELS FOR LINEAR ANALYTIC SYSTEMS HAVING MULTIPLE INPUTS;141
31.4;REALIZATION : SECOND ORDER;142
31.5;REALIZATION : HIGHER ORDER;142
31.6;AN APPLICATION OF TENSOR REALIZATION;142
31.7;
6.CONCLUSION;144
31.8;REFERENCES;144
31.9;APPENDIX: BRIEF REVIEW OF REALIZATION;145
31.10;ACKNOWLEDGEMENT;145
32;CHAPTER 25. THE APPLICATION OF A COMPUTER ALGEBRA SYSTEM TO THE ANALYSIS OF ACLASS OF NONLINEAR SYSTEMS;146
32.1;INTRODUCTION;146
32.2;GRAPHICAL FRONT-END FOR NONLINEAR SYSTEM DESIGN;146
32.3;CONTINUOUS SYSTEMS;147
32.4;SAMPLED-DATA SYSTEMS;149
32.5;OTHER WORK;150
32.6;CONCLUSIONS;151
32.7;ACKNOWLEDGEMENT;151
32.8;REFERENCES;151
33;CHAPTER 26. INPUT-OUTPUT APPROXIMATIONS OF DYNAMICAL SYSTEMS;152
33.1;INTRODUCTION;152
33.2;NOTATION;152
33.3;MODELLING AS A MIN-MAX PROBLEM;153
33.4;THE EXISTENCE OF AN OPTIMALMODEL;153
33.5;GRADIENT COMPUTATION;155
33.6;CONCLUSIONS;157
33.7;ACKNOWLEDGEMENTS;157
33.8;REFERENCES;157
34;CHAPTER 27. HARMONIC BALANCING USING A VOLTERRA INPUT OUTPUT DESCRIPTION;158
34.1;INTRODUCTION;158
34.2;SYSTEM DESCRIPTION;158
34.3;CONDITIONS FOR AN OSCILLATION;158
34.4;PARTITION OF THE EQUATIONS;159
34.5;THE ALGORITHM;160
34.6;THE BALANCE EQUATIONS;160
34.7;A SPECIAL CASE;160
34.8;EXAMPLES;161
34.9;CONCLUSIONS;162
34.10;ACKNOWLEDGMENTS;162
34.11;REFERENCES;162
35;CHAPTER 28. SYMBOLIC CALCULUS AND VOLTERRA SERIES;164
35.1;1. WORDS , LANGUAGS AND FORMAL PWER SERIES ([1]);164
35.2;2. CALCULUS OF THE FORMAL POWER SERIES EVALUATION;165
35.3;3. CHEN SERIES ([4], [15]);167
35.4;4. REALIZATION;168
35.5;5. REFERENCES;169
36;CHAPTER 29. LOCAL AND MINIMAL REALIZATION OF NONLINEAR DYNAMICAL SYSTEMS AND LYNDON WORDS;170
36.1;INTRODUCTION;170
36.2;FORMAL POWER SERIES;170
36.3;LYNDON WORDS;171
36.4;VECTOR FIELDS ANDDYNAMICAL SYSTEMS;172
36.5;SYSTEM GEOMETRY ANDFORMAL POWDER SERIES;172
36.6;REALIZATION OFDYNAMICAL SYSTEMS;173
36.7;BIBLIOGRAPHIE;175
37;CHAPTER 30. AN INVESTIGATION OF LINEAR STABILIZABILITY OF PLANAR BILINEAR SYSTEMS;176
37.1;1.INTRODUCTION;176
37.2;2. STATEMENT OF THE PROBLEM;176
37.3;3. THE CASE (2.1);177
37.4;4. THE CASE (2.2);177
37.5;Proof;178
37.6;5. THE CASE (2.3);178
37.7;REFERENCES;181
38;CHAPTER 31. VIBRATIONAL CONTROL OF NONLINEAR TIME LAG SYSTEMS: VIBRATIONAL STABILIZATION AND TRANSIENT BEHAVIOR*;182
38.1;I. INTRODUCTION;182
38.2;II. VIBRATIONAL STABILIZATION;183
38.3;III. TRANSIENT BEHAVIOR ANALYSIS OF VIBRATIONALLY CONTROLLED NONLINEAR TIME LAG SYSTEMS;185
38.4;IV. CONCLUSIONS;187
38.5;REFERENCES;187
38.6;APPENDIX;187
39;CHAPTER 32.STABILIZABILITY OF NONHOLONOMIC CONTROL SYSTEMS;188
39.1;1. INTRODUCTION;188
39.2;2. HAMILTONIAN CONTROL SYSTEMS ANDNONHOLONOMIC CONSTRAINTS;188
39.3;3. EQUILIBRIA OF NONHOLONOMIC CONTROL SYSTEMS;190
39.4;4. STABILIZABILITY;190
39.5;5. CONCLUDING REMARKS;192
39.6;REFERENCES;193
40;CHAPTER 33. A LYAPUNOV APPROACH TO STABILIZE FEEDBACK LINEARIZED NONLINEAR SYSTEMS WITH DISTURBANCES;194
40.1;INTRODUCTION;194
40.2;QUASI LINEAR SYSTEMS;194
40.3; STATEMENT OF THE PROBLEM;195
40.4;MAIN RESULT;195
40.5;DESIGN PROCEDURE;197
40.6;EXAMPLE;197
40.7;CONCLUSION;198
40.8;REFERENCES;198
41;CHAPTER 34. LOCAL ASYMPTOTIC STABILIZATION OF TWO DIMENSIONAL POLYNOMIAL SYSTEMS;200
41.1;1 Introduction;200
41.2;2 Preliminaries;200
41.3;3 Asymptotic stabilization;201
41.4;References;203
42;CHAPTER 35. NONLINEAR STABILIZATION OF A CLASS OF SINGULARLY PERTURBED UNCERTAIN SYSTEMS;204
42.1;INTRODUCTION;204
42.2;PROBLEM STATEMENT;204
42.3;STRUCTURE OF THE CONTROLLERA N D PROOF OF STABILITY;205
42.4;CONCLUSIONS;207
42.5;APPENDIX;207
42.6;REFERENCES;207
43;CHAPTER 36. STABILITY ANALYSIS OF QUADRATIC SYSTEMS;210
43.1;1. Introduction;210
43.2;2· Problem statement;210
43.3;3. Selection of the Lyapunov function;211
43.4;4. Domain of attraction;212
43.5;5. Some optimization problems;212
43.6;6. Numerical examples;213
43.7;7. Conclusions;213
43.8;Acknowledgements;214
43.9;References;214
44;CHAPTER 37. A GENERALISATION OF THE SMALL-GAIN THEOREM FOR NONLINEAR FEEDBACK SYSTEMS;216
44.1;NTRODUCTION;216
44.2;INPUT- OUTPUT STABILITY;216
44.3;FEEDBACK SYSTEM STABILITY;217
44.4;CONCLUSIONS;219
44.5;ACKNOWLEDGEMENT;219
44.6;REFERENCES;219
45;CHAPTER 38. ON A NONLINEAR MULTIVARIABLE SERVOMECHANISM PROBLEM;222
45.1;1. Introduction;222
45.2;2. Problem Description and Hypotheses;222
45.3;3. Feedback Control Law;223
45.4;4. Closed-Loop System Properties;225
45.5;5. Concluding Remarks;226
45.6;6. References;226
46;CHAPTER 39. GLOBAL DYNAMICS ACHIEVABLE BY FEEDBACK CONTROLS: SOME PRELIMINARY;228
46.1;1. INTRODUCTION;228
46.2;2. DEFINITIONS AND CLASSIFICATION RESULTS;229
46.3;3. EQUILIBRIUM POINTS;230
46.4;4. LIMIT CYCLES;231
46.5;5. SELECTION OF FEEDBACK CONTROLS;232
46.6;6. CONCLUSIONS;232
46.7;REFERENCES;232
47;CHAPTER 40. ON THE ABSOLUTE STABILITY CRITERIA IMPROVING AND ABSOLUTE STABILITY REGIONS CONSTRUCTION;234
47.1;INTRODUCTION;234
47.2;THE IMPROVED CRITERION;234
47.3;THE ABSOLUTE STABILITY CRITERION CONSTRUCTION;236
47.4;EXAMPLE;236
47.5;The polinomial;237
47.6;CONCLUSION;237
47.7;REFERENCES;237
48;CHAPTER 41. AN APPROACH TO NONLINEAR MULTIVARIABLE CONTROL SYSTEMS DESIGN;240
48.1;INTRODUCTION;240
48.2;PROBLEM STATEMENT AND SOME RELATED MINIMIZATION PROBLEMS;240
48.3;THE GENERAL FORM OF CONTROL;241
48.4;BILINEAR SYSTEMS;242
48.5;EXAMPLE;242
48.6;CONCLUSIONS;243
48.7;REFERENCES;243
49;CHAPTER 42. NONSINGULAR AND STABLE ADAPTIVE CONTROL OF DISCRETE-TIME BILINEAR SYSTEMS;244
49.1;INTRODUCTION;244
49.2;SYSTEM MODEL;244
49.3;PARAMETER ESTIMATION;245
49.4;ONE- STEP AHEAD CONTROLLER DESIGN;245
49.5;STABILITY ANALYSIS;247
49.6;EXAMPLE;248
49.7;CONCLUSIONS;248
49.8;REFERENCES;248
50;CHAPTER 43. DIRECT ADAPTIVE CONTROL OF NONLINEAR SYSTEMS;250
50.1;1. INTRODUCTION;250
50.2;2. SYSTEM DESCRIPTION;250
50.3;3. ASYMPTOTIC PROPERTIES;251
50.4;4. NONLINEAR PLANT;251
50.5;5. CONCLUDING DISCUSSION;252
50.6;REFERENCES;253
51;CHAPTER 44. DISCRETE TIME ADAPTIVE CONTROL FOR A CLASS OF NONLINEAR CONTINUOUS SYSTEMS;254
51.1;ABSTRACT
;254
51.2;1. INTRODUCTION
;254
51.3;2. SYSTEM DESCRIPTION IN CONTINUOUS TIME
;254
51.4;3.EXACT SAMPLING OF NON LINEAR CONTINUOUS SYSTEMS ;255
51.5;4.STATEMENT OF THE ADAPTIVE CONTROL PROBLEM ;255
51.6;5. DISCRETE PARAMETER ESTIMATION
;256
51.7;6. ADAPTIVE r-LINEARIZING CONTROL
;256
51.8;7. CONCLUSIONS
;258
51.9;APPENDIX;259
51.10;REFERENCES
;259
52;CHAPTER 45. ROBUSTNESS OF ADAPTIVE NONLINEAR CONTROL UNDER AN EXTENDED MATCHING CONDITION1;260
52.1;1. INTRODUCTION AND PROBLEM STATEMENT;260
52.2;2. ADAPTIVE REGULATION;261
52.3;3. ROBUSTNESS OF ADAPTIVE REGULATION;264
52.4;4. CONCLUSIONS;265
52.5;REFERENCES;265
52.6;APPENDIX;265
53;CHAPTER 46. SWITCHING STABILIZATION CONTROL FOR A SET OF NONLINEAR TIME-VARYING SYSTEMS;266
53.1;1. Introduction;266
53.2;2. Set of the plants;266
53.3;3. Construction of the switching controIler ;267
53.4;4. Quadratic stabilization and an example;268
53.5;5. C
onelusions;269
53.6;ACKNOWLEDGEMENT;269
53.7;REFERENCE;269
54;CHAPTER 47. NONLINEAR DYNAMICS OF ADAPTIVE LINEAR SYSTEMS: AN ELEMENTARY EXAMPLE;272
54.1;1 Introduction;272
54.2;2 The frozen system;273
54.3;3 Equilibrium point and period-2 solutions;273
54.4;4 Locally invariant sets;274
54.5;5 Behavior of the solutions: technical results;275
54.6;6 Behavior of the solutions: interpretation;276
54.7;7 References;277
55;CHAPTER 48. ASYMPTOTIC LINEARIZATION OF UNCERTAIN SYSTEMS BY MEANS OF APPROXIMATE SLIDING MODES;278
55.1;INTRODUCTION;278
55.2;THE PROPOSED APPROACH FOR MINIMUM PHASE SYSTEMS;279
55.3;THE CASE OF UNAVAILABLE OUTPUT DERIVATIVES;280
55.4;CONCLUSIONS;281
55.5;REFERENCES;281
56;CHAPTER 49. ON THE BEHAVIOR OF VARIABLE STRUCTURE CONTROL SYSTEMS NEAR THE SLIDING MANIFOLD;284
56.1;INTRODUCTION;284
56.2;GENERALIZED APPROXIMABILITY;284
56.3;CONTROL SYSTEMS FULFILLING GENERALIZED APPROXIMABILITY;285
56.4;LINEAR TIME-INVARIANT SYSTEMS;285
56.5;REFERENCES;285
56.6;ON DISCRETE-TIME SLIDING MODES;288
56.7;INTRODUCTION;288
56.8;DISCRETE-TIME SLIDING MODE DEFINITION;288
56.9;SLIDING MODES SIMULATION;289
56.10;DSM CONTROL ALGORITHMS;290
56.11;REFERENCES;291
57;CHAPTER 50. A NEW METHOD FOR SUPPRESSING CHATTERING IN VARIABLE STRUCTURE FEEDBACK CONTROL SYSTEMS;294
57.1;INTRODUCTION;294
57.2;DESIGN METHOD FOR SLIDING CONTROLLER;294
57.3;Properties of a quasi-sliding mode;296
57.4;Example;298
57.5;Further modification of continuous control law using integral transformation;298
57.6;CONCLUSIONS;298
57.7;APPENDIX;299
57.8;REFERENCES;299
58;CHAPTER 51. SLIDING OBSERVER DESIGN FOR NONLINEAR STATE ESTIMATION;300
58.1;INTRODUCTION;300
58.2;DESIGN OF SLIDING OBSERVERS;300
58.3;The Main Result for Robust Sliding Observer Design;301
58.4;First Design Procedure;301
58.5;Second Design Procedure;302
58.6;NUMERICAL EXAMPLE;303
58.7;CONCLUDING REMARKS;304
58.8;REFERENCES;305
59;CHAPTER 52. TWO CHARACTERIZATIONS OF OPTIMAL TRAJECTORIES FOR MEYER PROBLEM;306
59.1;Introduction;306
59.2;1 Value function;307
59.3;2 Regularity of optimal feedback;308
59.4;3 Optimal trajectories and viability theory;308
59.5;4 End point constraints;309
59.6;References;310
60;CHAPTER 53. ON THE SOLUTION OF OPTIMIZATION PROBLEMS WITH INCLUSION CONSTRAINTS;312
60.1;1. INTRODUCTION AND NOTATIONS;312
60.2;2. EXACT PENALIZATION;313
60.3;3. APPLICATION TO DYNAMIC PROCESSES;314
60.4;CONCLUSION;317
60.5;REFERENCES;317
61;CHAPTER 54. OPTIMAL CONTROL BY POLYNOMIAL APPROXIMATION: THE DISCRETE TIME CASE;318
61.1;INTRODUCTION;318
61.2;TENSOR BACKGROUND;318
61.3;PROBLEM STATEMENT;320
61.4;PROBLEM SOLUTION;320
61.5;SOLUTION FOR HIGHER ORDER TERMS;322
61.6;SPECIAL CASES;323
61.7;ACKNOWLEDGEMENTS;323
61.8;REFERENCES;323
62;CHAPTER 55. RELAXATION AND OPTIMAL CONTROL OF NONLINEAR DISTRIBUTED PARAMETER SYSTEMS;324
62.1;INTRODUCTION;324
62.2;EXISTENCE OF OPTIMAL SOLUTIONS;324
62.3;RELAXED SYSTEM;325
62.4;NECESSARY CONDITIONS;326
62.5;REFERENCES;327
63;CHAPTER 56. THE DISCRETE MAXIMUM PRINCIPLE: TWO METHODS OF PROOF;328
63.1;INTRODUCTION;328
63.2;TKE DISCRETE MAXIMUM PRINCIPLE FOR PROBLEMS WITH LIPSCHITZIAN FUNCTIONS;328
63.3;VARIATIONAL APPROACH TO THE DISCRETE MAXIMUM PRINCIPLE;331
63.4;ALGORITHM BASED ON THE DISCRETE MAXIMUM PRINCIPLE;333
63.5;CONCLUSION;334
63.6;REFERENCES;334
64;CHAPTER 57. NECESSARY CONDITIONS FOR OPTIMALITY VIA VOLTERRA APPROXIMATIONS;336
64.1;§1 - Introduction;336
64.2;§2 - Notations and abstract results;336
64.3;§3. Applications;339
64.4;References;341
65;CHAPTER 58. A NOVEL COMPUTER APPROACH TO OPTIMAL FEEDBACK CONTROL OF BILINEAR SYSTEMS;342
65.1;INTRODUCTION;342
65.2;OPTIMAL CONTROL PROBLEM;342
65.3;COMPUTER APPROACH;343
65.4;EULERS METHOD OF CONVERGENCE ACCELERATION;344
65.5;EXAMPLE;345
65.6;DISCUSSIONS AND EXTENSIONS;346
65.7;REFERENCES;346
66;CHAPTER 59. ROBUST NONLINEAR CONTROL AND OBSERVER SCHEMES FOR A CHEMICAL REACTOR;348
66.1;INTRODUCTION;348
66.2;SLIDING MODES AND THEIR APPLICATION TO
NONLINEAR SYSTEMS;348
66.3;ATPLI CATION TO A CONTINUOUS STIRRED TANK REACTOR;350
66.4;Sliding Observer Design;351
66.5;SIMULATION RESULTS;351
66.6;CONCLUSIONS;352
66.7;APPENDIX A;353
66.8;REFERENCES;353
67;CHAPTER 60. CONTROL OF A CONTINUOUS BIOPROCESS BY SIMPLE ALGORITHMS OF "P" AND"L/A" TYPE;354
67.1;NTRODUCTION;354
67.2;§1.- BRIEF PRESENTATION OF L/A CONTROL;354
67.3;§.2 - A CONTINUOUS BIOPROCESS;356
67.4;§.3 - REGULATION OF BIOMASS CONCENTRATION B YFIXED AND ADAPTIVE "P" CONTROLLERS;356
67.5;§.4 - REGULATION OF BIOMASS CONCENTRATION BY A MINIMAL L/A CONTROLLER;358
67.6;CONCLUSION;359
67.7;REFERENCES;359
68;CHAPTER 61. MODEL PREDICTIVE CONTROL OF NONLINEAR PROCESSES IN THE PRESENCE OF CONSTRAINTS;360
68.1;INTRODUCTION;360
68.2;THE ALGORITHM;360
68.3;SIMULATION RESULTS;361
68.4;COMPARISON AND DISCUSSION;362
68.5;CONCLUSIONS;362
68.6;ACKNOWLEDGEMENTS;362
68.7;LITERATURE CITED;362
69;CHAPTER 62. QUALITATIVE AND CONTROL BEHAVIOR OF A CLASS OF CHEMICAL AND BIOLOGICAL SYSTEMS;366
69.1;INTRODUCTION;366
69.2;PROBLEM FORMULATION;366
69.3;QUALITATIVE BEHAVIOR;367
69.4;CONTROLLABILITY AND STABILIZABILITY;368
69.5;REFERENCES;369
70;CHAPTER 63. NONLINEAR PROCESS CONTROL: AN ADAPTIVE APPROACH WHICH USES PHYSICAL MODELS;372
70.1;INTRODUCTION;372
70.2;CONTROLLING THE CSTR;373
70.3;THE EFFECT OF MISMATCH AND IMPLEMENTATION ISSUES ;375
70.4;REFERENCES:;376
70.5;
SUMMARY AND CONCLUSIONS;376
70.6;NOMENCLATURE
;377
71;CHAPTER 65. THE DESIGN OF LINEARIZING OUTPUTS FOR INDUCTION MOTORS;378
71.1;Introduction;378
71.2;Induction motor model;378
71.3;Full lineariza
tion via dynamic feedback;379
71.4;Input - output linearization via dynamic feedback;380
71.5;Conclusions;382
71.6;References;382
72;CHAPTER 66. THE RADIO-FREQUENCY MAGNETIC FIELD DESIGN IN BIOMEDICINE:NUCLEAR MAGNETIC RESONANCE IMAGING;384
72.1;1 - INTRODUCTION;384
72.2;2 - THE BASIC EOUATIONS;384
72.3;3 - THE LIE ALGEBRAT STRUCTURE OF THE EQUATION;385
72.4;4 - THE DESIGN OF THE COMMAND;385
72.5;5- CONCLUSION;387
72.6;Appendix;387
72.7;References ;387
73;CHAPTER 67. MODELLING AND CONTROL OF A TWO-AXIS ROBOT WITH FLEXIBLE LINKS;388
73.1;INTRODUCTION;388
73.2;THE MODEL;388
73.3;CONTINUOUS-TIME CONTROL;389
73.4;CONCLUSION;392
73.5;REFERENCES;392
73.6;APPENDIX I;393
73.7;APPENDIX II;393
74;CHAPTER 68. SLIDING OBSERVERS FOR ROBOT MANIPULATORS;394
74.1;1. INTRODUCTION;394
74.2;2. PROBLEM FORMULATION;394
74.3;3. OBSERVER DESIGN;396
74.4;4. DESIGN SIMPLIFICATIONS;398
74.5;5. CONCLUSIONS;399
74.6;6. REFERENCES
;399
75;CHAPTER 69. NONLINEAR CONTROLLER DESIGN FOR FLIGHT CONTROL SYSTEMS ;400
75.1;Introduction;400
75.2;I .Modeling of Aircraft Dynamics;400
75.3;II . Linearization by State Feedback;401
75.4;III. A Formal Approach to the Controlof Slightly Non-minimum PhaseSystems;404
75.5;Conclusion;405
75.6;References;405
76;CHAPTER 70. LYAPUNOV DESIGN FOR ADAPTIVE CONTROL OF ROBOTS;406
76.1;INTRODUCTION;406
76.2;PROBLEM STATEMENT;406
76.3;CONCLUSIONS;410
76.4;APPENDIX — PROOF OF LEMMA 1;410
76.5;REFERENCES;411
77;CHAPTER 71. NONLINEAR IDENTIFICATION ANDOBSERVER BASED COMPENSATION OF FRICTION IN MECHANICAL SYSTEMS;412
77.1;1. INTRODUCTION;412
77.2;2. MODELING AND IDENTIFICATION OF THE PROCESS DYNAMICS;412
77.3;3. DESIGN OF A LINEAR AND NONLINEAR FRICTION OBSERVER;414
77.4;4. Compensation of the estimated friction;415
77.5;5. EXAMPLE;416
77.6;6. CONCLUSIONS;417
77.7;7. REFERENCES;417
78;CHAPTER 72. DESIGN OF NONLINEAR OBSERVERS FOR ELASTIC JOINT ROBOTS;418
78.1;INTRODUCTION;418
78.2;MANIPULATOR MODEL;418
78.3;OBSERVER DESIGN;420
78.4;APPLICATION TO A THREE LINK ROBOT;422
78.5;CONCLUSIONS;423
78.6;REFERENCES;423
79;AUTHOR INDEX;424
80;KEYWORD INDEX;426
81;SYMPOSIA VOLUMES;428