Fliess Nonlinear Control Systems Design 1992

Selected papers from the 2nd IFAC Symposium, Bordeaux, France, 24 - 26 June 1992
1. Auflage 2016
ISBN: 978-1-4832-9875-7
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 498 Seiten, Web PDF

Reihe: IFAC Symposia Series

This volume represents most aspects of the rich and growing field of nonlinear control. These proceedings contain 78 papers, including six plenary lectures, striking a balance between theory and applications. Subjects covered include feedback stabilization, nonlinear and adaptive control of electromechanical systems, nonholonomic systems. Generalized state space systems, algebraic computing in nonlinear systems theory, decoupling, linearization and model-matching and robust control are also covered.

Autoren/Hrsg.

Fliess, M.

Inhaltsverzeichnis

1;Front Cover;1
2;Nonlinear Control Systems Design 1992;4
3;Copyright Page;5
4;Table of Contents;10
5;PREFACE;8
6;PART I: PLENARY LECTURES;16
6.1;CHAPTER 1. RECENT ADVANCES IN THE STABILIZATION PROBLEM FOR LOW DIMENSIONAL SYSTEMS;16
6.1.1;1 Introduction;16
6.1.2;2 Basic Definitions and Notation;16
6.1.3;3 Necessary Conditions for the Asymptotic Stabilization of Nonlinear Systems;17
6.1.4;4 Sufficient Conditions for Asymptotic Stabilizability of Low Dimensional Systems;19
6.1.5;5 Concluding Remarks;21
6.1.6;6 Acknowledgements;21
6.1.7;References;21
6.2;CHAPTER 2. NONLINEAR H8 CONTROL AND HAMILTON-JACOBI INEQUALITIES;24
6.2.1;1 Introduction;24
6.2.2;2 Formulation of the standard Hoo optimal control problem for nonlinear systems;24
6.2.3;3 L2-gain analysis of nonlinear systems and the nonlinear Bounded Real Lemma;25
6.2.4;4 State feedback Hoo control;27
6.2.5;5 Necessary conditions for H8 control by dynamic output feedback;28
6.2.6;6 Some sufficient conditions;28
6.2.7;References;29
6.3;CHAPTER 3. SYSTEMS COMBINING LINEARITY AND SATURATIONS, AND RELATIONS OF "NEURAL NETS";30
6.3.1;1. Introduction;30
6.3.2;2. ls-Systems;31
6.3.3;3. sl-Systems;32
6.3.4;4. s-Systems;32
6.3.5;5. Remarks;35
6.3.6;References;35
6.4;CHAPTER 4. A DYNAMICAL SYSTEMS APPROACH TO CONTROL;38
6.4.1;I. Introduction;38
6.4.2;II. Dynamical Systems;39
6.4.3;III. Control Flows;40
6.4.4;IV. Global Analysis and Complex Behavior of Control Systems;41
6.4.5;V. Robust Feedback via Lyapunov Exponents;43
6.4.6;REFERENCES;44
6.5;CHAPTER 5. DYNAMICAL DISCONTINUOUS FEEDBACK CONTROL OF NON-LINEAR SYSTEMS;46
6.5.1;1. INTRODUCTION;46
6.5.2;2. DYNAMICAL DISCONTINUOUS FEEDBACK CONTROL OF NONLINEAR SYSTEMS;46
6.5.3;3. SOME APPLICATION EXAMPLES;48
6.5.4;4. CONCLUSIONS;50
6.5.5;REFERENCES;50
6.6;CHAPTER 6. REMARKS ON SOME APPLICATIONS OF NONLINEAR CONTROL TECHNIQUES TO CHEMICAL PROCESSES;52
6.6.1;1 Introduction;52
6.6.2;2 Distillation;52
6.6.3;3 Stirred tank reactors;54
6.6.4;4 Conclusion;56
6.6.5;References;56
7;PART II: FEEDBACK STABILIZATION;58
7.1;CHAPTER 7. STABILIZATION WITH RESPECT TO NONCOMPACT SETS: LYAPUNOV CHARACTERIZATIONS AND EFFECT OF BOUNDED INPUTS;58
7.1.1;1. Introduction;58
7.1.2;2. Set Stability;58
7.1.3;3. Control Problem;62
7.1.4;References;63
7.2;CHAPTER 8. STABILIZATION OF LINEAR SYSTEMS WITH BOUNDED CONTROLS;66
7.2.1;1. Introduction;66
7.2.2;2. Proof of the main theorem;67
7.2.3;3. The Proofs of Lemma 2.1 and Lemma 2.2;69
7.2.4;4. Output feedback;71
7.2.5;References;71
7.3;CHAPTER 9. EXAMPLES OF PIECEWISE SMOOTH STABILIZATION OF DRIFTLESS NL SYSTEMS WITH LESS INPUTS THAN STATES;72
7.3.1;1 Introduction;72
7.3.2;2 A two-dimensional, single control system;73
7.3.3;3 The 2-DOF mobile example;73
7.3.4;4 Attitude stabilization of a rigid body;75
7.3.5;5 Conclusions;76
7.3.6;References;76
7.4;CHAPTER 10. LYAPUNOV DESIGN OF A DYNAMIC OUTPUT FEEDBACK FOR SYSTEMS LINEAR IN THEIR UNMEASURED STATE COMPONENTS;78
7.4.1;1 Introduction and Problem statement;78
7.4.2;2 Assumptions;79
7.4.3;3 Lyapunov design of a dynamic output feedback;80
7.4.4;4 Properties of the closed loop system;81
7.4.5;5 Examples;82
7.4.6;6 Concluding remarks;82
7.4.7;Acknowledgements;83
7.4.8;References;83
8;PART III: NONLINEAR AND ADAPTIVE CONTROL OF ELECTRO MECHANICAL SYSTEMS;84
8.1;CHAPTER 11. MODELING THE EFFECTS OF MAGNETIC SATURATION ON ELECTRICAL MACHINE CONTROL SYSTEMS;84
8.1.1;1 Introduction;84
8.1.2;2 Magnetic Circuit Modeling;84
8.1.3;3 Blondel-Park Transformation;86
8.1.4;4 Torque Production;86
8.1.5;5 Field-Oriented Control;86
8.1.6;6 Flux Observers;88
8.1.7;7 Indirect Control;90
8.1.8;8 Simulation Results;90
8.1.9;9 Conclusion;91
8.1.10;References;91
8.2;CHAPTER 12. DECOMPOSED ALGORITHMS FOR SPEED AND PARAMETER ESTIMATION IN INDUCTION MACHINES;92
8.2.1;1. Introduction;92
8.2.2;2. Equation-Error Formulation;92
8.2.3;3· Decomposed Algorithms for Batch Estimation;93
8.2.4;4. Experimental Results: Batch Estimation;93
8.2.5;5· Conditioning of the Problem;94
8.2.6;6. Coupling Among Parameters;95
8.2.7;7. Recursive Decomposed Algorithms;96
8.2.8;8. Conclusions and Comments;96
8.2.9;9. Acknowledgments;97
8.2.10;References;97
8.3;CHAPTER 13. NONLINEAR FEEDBACK AND CONTROL STRATEGY OF THE INDUCTION MOTOR;98
8.3.1;INTRODUCTION;98
8.3.2;MATHEMATICAL MODELS OF THE INDUCTION MOTOR;98
8.3.3;NONLINEAR FEEDBACK AND THE CONTROL SYSTEM;101
8.3.4;RESULTS OF SIMULATIONS;102
8.3.5;CONCLUSIONS;102
8.3.6;REFERENCES;103
9;PART IV: NONHOLONOMIC SYSTEMS;104
9.1;CHAPTER 14. THE GEOMETRY OF NON-HOLONOMIC SYSTEMS;104
9.1.1;Introduction;104
9.1.2;Lagrangian Mechanics;104
9.1.3;The Maximum Principle;105
9.1.4;The Maximum Principle is a restatement of the Hamiltonian formulation of the Lagranges Principle;105
9.1.5;The Elastic Energy of a Curve;107
9.1.6;References;109
9.2;CHAPTER 15. ANHOLONOMY IN THE CONTROL OF KINEMATICALLY REDUNDANT MECHANISMS WITH FLEXIBLE COMPONENTS;110
9.2.1;1 Introduction;110
9.2.2;2 Resolution of Kinematic Redundancy Using Acceleration Constraints;111
9.2.3;3 Nonholonomic Motion Planning for Elastic Manipulators;113
9.2.4;4 Conclusion;115
9.2.5;References;115
9.3;CHAPTER 16. NILPOTENT INFINITESIMAL APPROXIMATIONS TO A CONTROL LIE ALGEBRA;116
9.3.1;1 Accessibility and Controllability;116
9.3.2;2 Regular and Singular Points;117
9.3.3;3 The Notion of Local Order Attached to a System of Vector Fields;117
9.3.4;4 Order and Brackets;118
9.3.5;5 Privileged Coordinates;120
9.3.6;6 The Nilpotent Lie Algebra Tangent at x to a Control Lie Algebra;122
9.3.7;7 Controllability of Polynomial Vector Fields Is Decidable;123
9.3.8;References;123
9.4;CHAPTER 17. STABILIZATION AND TRACKING FOR NONHOLONOMIC CONTROL SYSTEMS USING TIME-VARYING STATE FEEDBACK;124
9.4.1;1 Introduction;124
9.4.2;2 Stabilization;125
9.4.3;3 Tracking;126
9.4.4;4 Simulation comparisons;127
9.4.5;References;128
10;PART V: CONTROL OF NON-HOLONOMIC SYSTEMS;130
10.1;CHAPTER 18. ON THE DYNAMICS AND CONTROL OF NONHOLONOMIC SYSTEMS ON RIEMANNIAN MANIFOLDS;130
10.1.1;1 Introduction;130
10.1.2;2 Holonomic Control Systems;130
10.1.3;3 Nonholonomic Systems;131
10.1.4;4 Symmetries;132
10.1.5;5 Reduction;132
10.1.6;6 Example: The Rolling Ball;133
10.1.7;7 Optimal Control;133
10.1.8;References;134
10.2;CHAPTER 19. ABNORMAL OPTIMAL CONTROLS AND OPEN PROBLEMS IN NONHOLONOMIC STEERING;136
10.2.1;1 Introduction;136
10.2.2;2 Abnormal Extremals;136
10.2.3;3 Hsu's observation: abnormals equal characteristics;138
10.2.4;4 Sufficiency and Open Problems;139
10.2.5;5 Time Optimal Curves Equal SubRiemannian Geodesies;139
10.2.6;6 Application of the Maximum Principle to the Three Problems;141
10.2.7;References;141
10.3;CHAPTER 20. OPTIMAL CONTROL AND ALMOST ANALYTIC FEEDBACK FOR SOME NONHOLONOMIC SYSTEMS;142
10.3.1;1. Introduction;142
10.3.2;2. Existence of FCL's;143
10.3.3;3. Almost analytic FCL's;144
10.4;CHAPTER 21. THE STRUCTURE OF OPTIMAL CONTROLS FOR A STEERING PROBLEM;150
10.4.1;1 Introduction;150
10.4.2;2 First derivative of the optimal control;150
10.4.3;3 Higher Order Derivatives of the Optimal Controls;152
10.4.4;4 Optimal Controls on Lie Groups;153
10.4.5;5 Sub-Riemannian Balls;154
10.4.6;References;155
11;PART VI: GENERALIZED STATE SPACE SYSTEMS;156
11.1;CHAPTER 22. REMARKS ON THE LINEARIZATION AROUND AN EQUILIBRIUM;156
11.1.1;1 Introduction;156
11.1.2;2 Conditions for linearization;157
11.1.3;3 Examples;157
11.1.4;References;157
11.2;CHAPTER 23. REMARKS ON EQUIVALENCE AND LINEARIZATION OF NONLINEAR SYSTEMS;158
11.2.1;1 Introduction;158
11.2.2;2 Equivalence;159
11.2.3;3 D-algebra of a system;159
11.2.4;4 Trajectories;160
11.2.5;5 Main result;160
11.2.6;6 Rational equivalence;161
11.2.7;7 Linearization;161
11.2.8;8 Example;162
11.2.9;References;162
11.3;CHAPTER 24. GENERALIZED STATE SPACE DESCRIPTIONS AND DIGITAL IMPLEMENTATION;164
11.3.1;1 Introduction;164
11.3.2;2 Notation and problem statement;164
11.3.3;3 Discrete time approximation of a state space description;164
11.3.4;4 A difference equation with bounded coefficients;165
11.3.5;5 Examples;166
11.3.6;6 Acknowledgement;167
11.3.7;References;167
11.4;CHAPTER 25. RATIONAL SYSTEM EQUIVALENCE, AND GENERALIZED REALIZATION THEORY;168
11.4.1;Introduction;168
11.4.2;1. Preliminaries;169
11.4.3;2. Rational system equivalence;170
11.4.4;3. Generalized rational realization theory;171
11.4.5;References;173
11.5;CHAPTER 26. ON DIFFERENTIALLY FLAT NONLINEAR SYSTEMS;174
11.5.1;1 Introduction;174
11.5.2;2 The differential fields approach;175
11.5.3;3 Equivalence by endogeneous dynamic feedback to linear controllable systems;175
11.5.4;4 Examples;176
11.5.5;5 Conclusion;177
11.5.6;References;177
12;PART VII: DYNAMIC FEEDBACK IN NONLINEAR SYSTEMS;180
12.1;CHAPTER 27. LINKS BETWEEN LOCAL CONTROLLABILITY AND LOCAL CONTINUOUS STABILIZATION;180
12.1.1;1. Introduction;180
12.1.2;2. Study of the linearized equation;182
12.1.3;3. Proof of Theorem 1.7;183
12.1.4;4. Sketch of the proof of Theorem 1.8;184
12.1.5;5. Links between the Sussmann condition and;185
12.1.6;Acknowledgments;185
12.1.7;References;185
12.2;CHAPTER 28. STRONG DYNAMIC INPUT-OUTPUT DECOUPLING: FROM LINEARITY TO NONLINEARITY;188
12.2.1;1 Introduction;188
12.2.2;2 Preliminaries;188
12.2.3;3 The nonlinear SDIODP and linearization;189
12.2.4;References;193
12.3;CHAPTER 29. AN ALGEBRAIC INTERPRETATION OF THE STRUCTURE ALGORITHM WITH AN APPLICATION TO FEEDBACK DECOUPLING;194
12.3.1;1 Introduction;194
12.3.2;2 Mathematical background;194
12.3.3;3 Linear systems;195
12.3.4;4 Nonlinear systems;197
12.3.5;References;198
13;PART VIII: NONLINEAR OBSERVERS AND MODEL-MATCHING;200
13.1;CHAPTER 30. MOVING HORIZON OBSERVERS†;200
13.1.1;1. Introduction;200
13.1.2;2. Notation and basic assumptions;201
13.1.3;3. An observer based on successive approximations of the initial condition;201
13.1.4;4. An optimization-based observer with output injection;204
13.1.5;5. Conclusions;205
13.1.6;6. References;205
13.2;CHAPTER 31. DYNAMIC FORMS AND THEIR APPLICATION TO CONTROL;206
13.2.1;1 Introduction;206
13.2.2;2 Scalar Forms;207
13.2.3;3 Vector Forms;208
13.2.4;4 Matrix Forms;208
13.2.5;5 Rotational Forms;209
13.2.6;6 Euler Angle Forms;210
13.2.7;7 Euler parameter form;210
13.2.8;8 Attitude Servo;210
13.2.9;9 Conclusion;211
13.2.10;References;211
13.3;CHAPTER 32. OBSERVER DESIGN IN THE TRACKING CONTROL PROBLEM OF ROBOTS;212
13.3.1;1. Introduction;212
13.3.2;2. Properties of Rigid Robot Manipulators;213
13.3.3;3. CTC with Velocity Estimator;213
13.3.4;4. PBC with Velocity Estimator;215
13.3.5;5. Conclusions;217
13.3.6;Acknowledgements;217
13.3.7;References;217
13.4;CHAPTER 33. ADAPTIVE LINEARIZATION BY DYNAMIC STATE FEEDBACK: A CASE STUDY;218
13.4.1;1 Introduction;218
13.4.2;2 Adaptive Linearization by Dynamic State Feedback;218
13.4.3;3 Control of a Robot Arm with Joint Elasticity;220
13.4.4;4 Simulation Results;222
13.4.5;References;223
13.5;CHAPTER 34. OPTIMAL MODEL MATCHING CONTROLLERS FOR LINEAR AND NONLINEAR SYSTEMS;224
13.5.1;1. Introduction;224
13.5.2;2. Linear Model Matching;224
13.5.3;3. Nonlinear Model Matching;227
13.5.4;References;229
13.6;CHAPTER 35. EXPONENTIAL OBSERVER DESIGN;230
13.6.1;1. Introduction;230
13.6.2;2. Exponential Observers;230
13.6.3;3. Example;232
13.6.4;References;232
14;PART IX: ALGEBRAIC COMPUTING IN NONLINEAR SYSTEMS THEORY;234
14.1;CHAPTER 36. IMPLEMENTING RITT'S ALGORITHM OF DIFFERENTIAL ALGEBRA;234
14.1.1;1 Introduction;234
14.1.2;2 Basic differential algebraic concepts;234
14.1.3;3 Basic building blocks of Ritt's algorithm;235
14.1.4;4 Ritt's algorithm;236
14.1.5;5 Modifications of Ritt's algorithm;237
14.1.6;6 Acknowledgement;238
14.1.7;References;238
14.2;CHAPTER 37. ON THE IDENTIFIABILITY OF DETERMINISTIC NONLINEAR MODEL PARAMETERS;240
14.2.1;Introduction;240
14.2.2;I. Preliminaries;241
14.2.3;II. On persistent trajectories and inputs;242
14.2.4;Ill. Examples;243
14.2.5;References;244
14.3;CHAPTER 38. RULE-BASED SELECTION OF NONLINEAR OBSERVER DESIGN METHODS;246
14.3.1;1 Introduction;246
14.3.2;2 Nonlinear Observation Problem;246
14.3.3;3 Rule Base for the Selection of Design Methods;247
14.3.4;4 Rule Interpreter for the Selection of Suitable Methods;248
14.3.5;5 Rule–Based Selection of Observer Design Methods in the MACSYMA Program MACNON;251
14.3.6;6 Example for a Rule–Based Observer Selection in MACNON;251
14.3.7;7 Conclusions;252
14.3.8;References;253
14.4;CHAPTER 39. MOTION PLANNING BY PIECEWISE CONSTANT OR POLYNOMIAL INPUTS;254
14.4.1;1 Introduction;254
14.4.2;2 Exponential Expansion;254
14.4.3;3 Sketch of the algorithm;255
14.4.4;4 Virtual Trajectory;255
14.4.5;5 Parametrized inputs;256
14.4.6;6 Input Identification;257
14.4.7;7 The Lyndon Encoding;258
14.4.8;References;259
14.5;CHAPTER 40. COMPUTING ITERATED DERIVATIVES ALONG TRAJECTORIES OF NONLINEAR SYSTEMS;260
14.5.1;1 Introduction;260
14.5.2;2 Basic presentation of some combinatorial tools;260
14.5.3;3 Computing the k-th derivative of output map;261
14.5.4;4 Conclusion;263
14.5.5;References;263
14.6;CHAPTER 41. COMBINATORICS OF REALIZATIONS OF NILPOTENT CONTROL SYSTEMS;266
14.6.1;1 Introduction;266
14.6.2;2 Nonlinear realization;267
14.6.3;3 Iterated brackets;269
14.6.4;References;270
14.7;CHAPTER 42. COMPUTER-AIDED ANALYSIS OF NONLINEAR OBSERVATION PROBLEMS;272
14.7.1;1 Introduction;272
14.7.2;2 Observability Conditions;272
14.7.3;3 Computer-Aided Analysis Observability;273
14.7.4;4 Observable System Structures;275
14.7.5;5 Example;276
14.7.6;6 Conclusions;277
14.7.7;References;277
15;PART X: DYNAMICAL AND CONTROL SYSTEMS;278
15.1;CHAPTER 43. HIGHER ORDER APPROXIMATE FEEDBACK LINEARIZATION ABOUT A MANIFOLD;278
15.1.1;Introduction;278
15.1.2;1 Preliminaries;278
15.1.3;2 Problem Formulation;279
15.1.4;3 Main Results;279
15.1.5;4 Example;282
15.1.6;Conclusion;283
15.1.7;References;283
15.2;CHAPTER 44. THE NORMAL FORMS, AVERAGING AND THE RESONANCE CONTROL OF NONLINEAR DYNAMICAL SYSTEMS;284
15.2.1;1. Introduction;284
15.2.2;2. Analysis and control of model of an elastic rotating bar;285
15.2.3;3. The saddle-node bifurcation on the aircraft dynamics;287
15.2.4;References;288
15.3;CHAPTER 45. ON CONTROL SETS AND FEEDBACK FOR NONLINEAR SYSTEMS;290
15.3.1;1. Introduction;290
15.3.2;2. Limit Behavior of Perturbed Differential Equations;291
15.3.3;3. Feedback in a Chemical Reactor Model;294
15.3.4;Acknowledgement;297
15.3.5;REFERENCES;297
15.4;CHAPTER 46. BIFURCATION CONTROL OF CHAOTIC DYNAMICAL SYSTEMS;298
15.4.1;1. Introduction;298
15.4.2;2. Thermal Convection Loop Model;299
15.4.3;3. Bifurcation Control of Convection Dynamics;300
15.4.4;4. Concluding Remarks;302
15.4.5;Acknowledgment;302
15.4.6;References;302
15.5;CHAPTER 47. ON THE CONTROL OF SINGULARLY PERTURBED NONLINEAR SYSTEMS;304
15.5.1;1 Introduction;304
15.5.2;2 Preliminaries;304
15.5.3;3 The control design;306
15.5.4;References;308
16;PART XI: APPLICATIONS;310
16.1;CHAPTER 48. STABILITY ANALYSIS AND CONTROL OF ROTATING STALL;310
16.1.1;1. Introduction;310
16.1.2;2. Preliminaries;311
16.1.3;4. Control of Rotating Stall;313
16.1.4;5. Simulations;313
16.1.5;Acknowledgment;314
16.1.6;References;314
16.2;CHAPTER 49. OPTIMAL CRONE CONTROL OF A TRACTOR HITCH SYSTEM;316
16.2.1;I - Introduction;316
16.2.2;II - Tractor hitch system as a study plant;316
16.2.3;Ill - Dynamic modelling ;317
16.2.4;IV - Control strategy;318
16.2.5;V - Synthesis of the regulator R(s);319
16.2.6;VI - Synthesis of the regulator K(s);321
16.2.7;VII - Simulation performances obtained with the non linear plant;321
16.2.8;VIII - Conclusion;322
17;PART XII: DECOUPLING, LINEARIZATION AND MODEL-MATCHING;324
17.1;CHAPTER 50. ON OUTPUT DECOMPOSED LINEARIZATION¹;324
17.1.1;1. Introduction;324
17.1.2;2. Output Decomposed Linearization;324
17.1.3;REFERENCES;329
17.2;CHAPTER 51. NONLINEAR CONTROL PROBLEMS AND SYSTEMS APPROXIMATIONS: A GEOMETRIC APPROACH;330
17.2.1;1. Introduction;330
17.2.2;2. Preliminaries;331
17.2.3;3. Controlled invariant distributions for Sk

and SK+1;331
17.2.4;4. Conclusions;334
17.2.5;References;334
17.3;CHAPTER 52. A DIFFERENTIAL ALGEBRAIC APPROACH TO THE CLASSICAL RIGHT MODEL MATCHING PROBLEM;336
17.3.1;1 Introduction;336
17.3.2;2 Input-output systems;336
17.3.3;3 Right model matching;337
17.3.4;4 Example;340
17.3.5;Acknowledgements;341
17.3.6;References;341
17.4;CHAPTER 53. QUALITATIVE ASPECTS OF ASYMPTOTIC NONLINEAR MODEL MATCHING;342
17.4.1;1. Introduction;342
17.4.2;2. Relationship Between Exact and Asymptotic Model Matching;342
17.4.3;3· Interdependence of the Properties of the Plant and Model;343
17.4.4;Acknowledgement;344
17.4.5;References;344
18;PART XIII: ALGEBRAIC AND GEOMETRIC METHODS;346
18.1;CHAPTER 54. ON A RANK INVARIANT OF ANALYTIC DISCRETE-TIME NONLINEAR SYSTEMS;346
18.1.1;1. Introduction;346
18.1.2;2. Main Results;346
18.1.3;3. Conclusions;348
18.1.4;Acknowledgement;348
18.1.5;References;348
18.2;CHAPTER 55. INVERTIBILITY OF DISCRETE-TIME SYSTEMS;350
18.2.1;1 Introduction;350
18.2.2;2 A summary of difference algebra;350
18.2.3;3 Linear systems;352
18.2.4;4 Nonlinear systems;353
18.2.5;References;354
18.3;CHAPTER 56. ON RATIONAL STATE SPACE REALIZATIONS;356
18.3.1;1 Introduction;356
18.3.2;2 Some Facts from Algebraic Geometry;356
18.3.3;3 Rational Realizations;357
18.3.4;4 Algebraic Observability and the Liiroth Problem;359
18.3.5;5 Some Examples;359
18.3.6;6 Computer Programs;360
18.3.7;Summary and Future Directions;360
18.3.8;Acknowledgements;360
18.3.9;References;360
18.4;CHAPTER 57. LOWERING ORDERS OF INPUT DERIVATIVES IN GENERALIZED STATE REPRESENTATIONS OF NONLINEAR SYSTEMS;362
18.4.1;1 Introduction to algebraic realization theory;362
18.4.2;2 Reduction of input derivation orders;362
18.4.3;3 Comments;364
18.4.4;4 Example;365
18.4.5;Acknowledgements;365
18.4.6;References;365
18.5;CHAPTER 58. NECESSARY CONDITIONS FOR THE REMOVAL OF SINGULARITIES WITH DYNAMIC STATE FEEDBACK;368
18.5.1;1. Introduction;368
18.5.2;2. On a Decoupling Martix Property of Closed Loop Sistems;369
18.5.3;3. Dynamic Feedback Laws at Singular Points;371
18.5.4;References;371
18.6;CHAPTER 59. PORT-CONTROLLED HAMILTONIAN SYSTEMS: MODELLING ORIGINS AND SYSTEMTHEORETIC PROPERTIES;374
18.6.1;1 Introduction;374
18.6.2;2 Port controlled Hamiltonian systems;374
18.6.3;3 Observability, controllability and minimal realizability;378
18.6.4;4 Conclusion;379
18.6.5;References;380
18.7;CHAPTER 60. SLIDING MODE CONTROL AND DIFFERENTIAL ALGEBRA;382
18.7.1;1. INTRODUCTION;382
18.7.2;2. A DYNAMICAL SLIDING MODE CONTROLLER EXAMPLE;382
18.7.3;3. A DIFFERENTIAL ALGEBRAIC APPROACH TO SLIDING MODE CONTROL OF NONLINEAR SYSTEMS;383
18.7.4;4. CONCLUSIONS AND SUGGESTIONS FOR FURTHER RESEARCH;386
18.7.5;REFERENCES;386
19;PART IVX: RECENT ADVANCES IN FEEDBACK STABILIZATION;388
19.1;CHAPTER 61. ON PASSIVE SYSTEMS: FROM LINEARITY TO NONLINEARITY;388
19.1.1;1. Introduction;388
19.1.2;2. Problem Formulation;389
19.1.3;3. A class of nonlinear systems;389
19.1.4;4. Main Result;390
19.1.5;5. Feedback equivalence to passive systems;391
19.1.6;Conclusions;393
19.1.7;Acknowlegments;393
19.1.8;References;393
19.2;CHAPTER 62. USING SATURATION TO STABILIZE A CLASS OF SINGLE-INPUT PARTIALLY LINEAR COMPOSITE SYSTEMS;394
19.2.1;1 Introduction;394
19.2.2;2 Feedforward Systems;394
19.2.3;3 General Results;395
19.2.4;4 Examples;397
19.2.5;5 Conclusion;399
19.2.6;References;399
19.3;CHAPTER 63. STABILIZATION OF NON LINEAR TWO DIMENSIONAL SYSTEMS: A BILINEAR APPROACH;400
19.3.1;1 Introduction and Notations;400
19.3.2;2 Classification and stabilization of planar bilinear systems;401
19.3.3;3 Bilinear approximation and applications;403
19.3.4;References;405
19.4;CHAPTER 64. LOCAL ADAPTIVE STABILIZATION OF A FIRST ORDER NONLINEAR SYSTEM WITHOUT LIPSCHITZ ASSUMPTIONS;406
19.4.1;I. INTRODUCTION;406
19.4.2;2. PROBLEM FORMULATION;406
19.4.3;3. PARAMETER ESTIMATION AND MODIFICATION PROCEDURE;407
19.4.4;4. CLOSED LOOP SYSTEM STATE SPACE REPRESENTATION;407
19.4.5;5. EXISTENCE AND UNIQUENESS OF SOLUTIONS;408
19.4.6;6. CONVERGENCE ANALYSIS;410
19.4.7;7. CONCLUSIONS;411
19.4.8;REFERENCES;411
19.5;CHAPTER 65. A REMARK ON THE DESIGN OF TIME-VARYING STABILIZING FEEDBACK LAWS FOR CONTROLLABLE SYSTEMS WITHOUT DRIFT;412
19.5.1;1 Introduction;412
19.5.2;2 Two different approaches;413
19.5.3;3 Main result;414
19.5.4;4 Conclusion;415
19.5.5;Aknowledgements;415
19.5.6;References;415
19.6;CHAPTER 66. SOME REMARKS ABOUT PERIODIC FEEDBACK STABILIZATION¹;418
19.6.1;1 INTRODUCTION;418
19.6.2;2 Preliminaries;419
19.6.3;3 Some connections between LAS and LAC: a brief review;420
19.6.4;4 Periodic feedback stabilization;421
19.6.5;5 An illustrative example;422
19.6.6;6 Acknowledgements;422
19.6.7;7 Appendix 1;422
19.6.8;References;423
19.7;CHAPTER 67. STABILIZATION OF NONLINEAR SYSTEMS BY USING INTEGRATORS;424
19.7.1;1. Introduction;424
19.7.2;2. Main results;425
19.7.3;3. Further generalizations;426
19.7.4;References;427
19.8;CHAPTER 68. SMOOTH STABILIZING TIME-VARYING CONTROL LAWS FOR A CLASS OF NONLINEAR SYSTEMS. APPLICATION TO MOBILE ROBOTS;428
19.8.1;1 Introduction;428
19.8.2;2 Proof of Theorem 1 when m=1;428
19.8.3;3 Proof of Theorem 1 when m>2;430
19.8.4;4 Application to mobile robots;430
19.8.5;References;433
19.9;CHAPTER 69. INVERSE OF LYAPUNOV'S SECOND THEOREM FOR MEASURABLE FUNCTIONS;434
19.9.1;1. Notations, general systems;434
19.9.2;2. Autonomous systems;437
19.9.3;3. No being of zero measure;439
19.9.4;References;439
19.10;CHAPTER 70. SLIDING MODES: THE CASE OF MULTIVARIABLE SYSTEMS NONLINEAR IN THE INPUTS;440
19.10.1;I. Introduction;440
19.10.2;II. Definitions and Notations;441
19.10.3;Construction of a control law. The case m=2;442
19.10.4;Conclusion;443
19.10.5;REFERENCES;443
20;PART XV: ROBUST CONTROL;446
20.1;CHAPTER 71. BACKSTEPPING DESIGN OF ROBUST CONTROLLERS FOR A CLASS OF NONLINEAR SYSTEMS;446
20.1.1;Introduction;446
20.1.2;Conclusion;450
20.1.3;References;450
20.2;CHAPTER 72. APPROXIMATE MATCHING OF NONLINEAR SYSTEMS VIA NONLINEAR H8 METHODS;452
20.2.1;1 Introduction;452
20.2.2;2 Definitions and assumptions;452
20.2.3;3 The case of full information;453
20.2.4;4 The case of output feedback;455
20.2.5;5 On the existence of solutions;456
20.2.6;References;458
20.3;CHAPTER 73. ADAPTIVE CONTROL OF A CLASS OF NONLINEAR SYSTEMS VIA THE ROBUST CONTROL APPROACH;460
20.3.1;1. Introduction;460
20.3.2;2. A review of nonlinear regulator theory;460
20.3.3;3. Main results;461
20.3.4;4. Conclusion;463
20.3.5;Acknowledgment;463
20.3.6;References;463
20.4;CHAPTER 74. OUTPUT FEEDBACK CONTROL OF A CLASS OF NONLINEAR SYSTEMS;464
20.4.1;1 Introduction;464
20.4.2;2 Basic results and definitions;464
20.4.3;3 Output feedback control;465
20.4.4;4 Output feedback control;466
20.4.5;5 Examples;469
20.4.6;References;469
21;PART XVI: ROBOTICS AND MECHANICAL SYSTEMS;470
21.1;CHAPTER 75. ROBUST CONTROL OF MECHANICAL SYSTEMS: AN EXPERIMENTAL STUDY;470
21.1.1;1 INTRODUCTION;470
21.1.2;2 THE CONTROLLERS;471
21.1.3;3 EXPERIMENTAL SETUP;471
21.1.4;4 DESIGN;473
21.1.5;5 EXPERIMENTS;473
21.1.6;6 CONCLUSIONS AND RECOMMENDATIONS;475
21.1.7;Acknowledgements;475
21.1.8;REFERENCES;476
21.2;CHAPTER 76. ATTITUDE CONTROL OF ARTICULATED, FLEXIBLE SPACECRAFT;478
21.2.1;1 Introduction;478
21.2.2;2 Lagrange's Equations & QUasi-Coordinates;478
21.2.3;3 Algorithmic Formulation of Kinetic Energy;479
21.2.4;4 Nonlinear Attitude Control via PFL;480
21.2.5;5 Summary of Simulation Results;481
21.2.6;6 Conclusions;482
21.2.7;References;483
21.3;CHAPTER 77. PATH FOLLOWING AND STABILIZATION OF A MOBILE ROBOT;486
21.3.1;1 Introduction;486
21.3.2;2 Exponential stabilization: the control law;486
21.3.3;3 Tracking a sequence of points;488
21.3.4;4 Conclusions;490
21.3.5;References;490
22;PART XVII: CONTROLLABILITY AND OPTIMAL CONTROL;492
22.1;CHAPTER 78. A NEW TYPE OF SUFFICIENT OPTIMALITY CONDITIONS FOR A NONLINEAR CONSTRAINED OPTIMAL CONTROL PROBLEM;492
22.1.1;1 Introduction;492
22.1.2;2 The abstract problem;493
22.1.3;3 A pointwise state and control constraint;497
22.1.4;References;498
23;AUTHOR INDEX;500
24;KEYWORD INDEX;502