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Dynamics, Bifurcations and Control : Lecture Notes in Control and Information Sciences - Fritz Colonius

Dynamics, Bifurcations and Control

Lecture Notes in Control and Information Sciences

By: Fritz Colonius (Editor), Lars Grune (Editor)

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Published: 11th January 2002
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This volume originates from the Third Nonlinear Control Workshop "- namics, Bifurcations and Control," held in Kloster Irsee, April 1-3 2001. As the preceding workshops held in Paris (2000) and in Ghent (1999), it was organized within the framework of Nonlinear Control Network funded by the European Union (http: //www.supelec.fr/lss/NCN). The papers in this volume center around those control problems where phenomena and methods from dynamical systems theory play a dominant role. Despite the large variety of techniques and methods present in the c- tributions, a rough subdivision can be given into three areas: Bifurcation problems, stabilization and robustness, and global dynamics of control s- tems. A large part of the fascination in nonlinear control stems from the fact that is deeply rooted in engineering and mathematics alike. The contributions to this volume reflect this double nature of nonlinear control. We would like to take this opportunity to thank all the contributors and the referees for their careful work. Furthermore, it is our pleasure to thank Franchise Lamnabhi-Lagarrigue, the coordinator of our network, for her s- port in organizing the workshop and the proceedings and for the tremendous efforts she puts into this network bringing the cooperation between the d- ferent groups to a new level. In particular, the exchange and the active p- ticipation of young scientists, also reflected in the Pedagogical Schools within the Network, is an asset for the field of nonlinear control

Bifurcation Problemsp. 1
Controlling an Inverted Pendulum with Bounded Controlsp. 3
Introductionp. 3
Description of the systemp. 4
Bounded control lawp. 5
Local nonlinear analysisp. 7
Numerical analysis of the global dynamical behaviorp. 8
Desired operating behaviourp. 14
Conclusionsp. 15
Referencesp. 16
Bifurcations of Neural Networks with Almost Symmetric Interconnection Matricesp. 17
Introductionp. 17
Neural network model and preliminariesp. 19
Limit cycles in a competitive neural networkp. 23
Hopf bifurcations in sigmoidal neural networksp. 26
Period-doubling bifurcations in a third-order neural networkp. 30
Conclusionp. 32
Referencesp. 32
Bifurcations in Systems with a Rate Limiterp. 37
Introductionp. 37
Behaviour of rate limitersp. 38
Describing function of rate limitersp. 41
Limit cycle analysis of systems with rate limitersp. 42
Bifurcations in systems with a rate limiterp. 43
Conclusionsp. 49
Referencesp. 50
Monitoring and Control of Bifurcations Using Probe Signalsp. 51
Introductionp. 51
Hopf bifurcationp. 52
Analysis of the effects of near-resonant forcingp. 54
Numerical examplep. 57
Combined Stability Monitoring and Controlp. 58
Detection of Impending Bifurcation in a Power System Modelp. 60
Conclusionsp. 64
Referencesp. 64
Normal Form, Invariants, and Bifurcations of Nonlinear Control Systems in the Particle Deflection Planep. 67
Introductionp. 67
Problem formulationp. 68
Normal form and invariantsp. 70
Bifurcation of control systemsp. 75
Bifurcation control using state feedbackp. 77
The cusp bifurcation and hysteresisp. 81
Other related issuesp. 83
Conclusionsp. 84
Referencesp. 85
Bifurcations of Reachable Sets Near an Abnormal Direction and Consequencesp. 89
Setup and definitionsp. 89
Asymptotics of the reachable setsp. 91
Applicationsp. 94
Referencesp. 98
Stabilization and Robustness101
Oscillation Control in Delayed Feedback Systemsp. 103
Introductionp. 103
Perturbations of linear retarded equationsp. 105
The harmonic oscillator under delayed feedbackp. 106
Controlling the amplitude and frequency of oscillationsp. 111
Conclusionp. 115
Referencesp. 115
Nonlinear Problems in Friction Compensationp. 117
Introductionp. 117
Conic analysis of uncertain frictionp. 121
Harmonic balancep. 124
Frequencial synthesis using QFTp. 127
Discussionp. 128
Referencesp. 129
Time-Optimal Stabilization for a Third-Order Integrator: a Robust State-Feedback Implementationp. 131
Introductionp. 131
Closed loop time-optimal stabilization for a third-order integratorp. 133
Sliding-mode implementation of the time-optimal controllerp. 137
Simulation resultsp. 141
Conclusionsp. 143
Referencesp. 144
Stability Analysis of Periodic Solutions via Integral Quadratic Constraintsp. 145
Introductionp. 145
A motivating examplep. 146
Problem formulation and preliminary resultsp. 148
Sufficient conditions for stability of periodic solutionsp. 151
Application examplep. 154
Conclusionsp. 156
Referencesp. 156
Port Controller Hamiltonian Synthesis Using Evolution Strategiesp. 159
Introductionp. 159
Port controlled Hamiltonian systemsp. 160
Controller designp. 160
Preliminaries on evolution strategiesp. 162
Evolutionary formulationp. 165
Case study - ball & beam systemp. 167
Conclusionsp. 169
Referencesp. 170
Feedback Stabilization and HOQ Control of Nonlinear Systems Affected by Disturbances: the Differential Games Approachp. 173
Introductionp. 173
Differential games approach to nonlinear Hoo controlp. 175
Other stability questionsp. 181
Building a feedback solution for nonlinear Hoo controlp. 182
Referencesp. 188
A Linearization Principle for Robustness with Respect to Time-Varying Perturbationsp. 191
Introductionp. 191
Preliminaries192
The discrete time casep. 195
Continuous timep. 197
Conclusion199
Referencesp. 200
Global Dynamics of Control Systemsp. 201
On Constrained Dynamical Systems and Algebroidsp. 203
Introduction: Constrained Hamiltonian systemsp. 203
What is a Lie algebroid?p. 205
Dirac structures and Port Controlled Hamiltonian systemsp. 208
Constrained mechanical systems and algebroidsp. 213
Control of constrained mechanical systemsp. 214
Referencesp. 216
On the Classification of Control Setsp. 217
Introductionp. 217
Basic definitionsp. 218
Strong inner pairsp. 219
The dynamic indexp. 221
The index of a control set near a periodic orbitp. 224
Referencesp. 230
On the Frequency Theorem for Nonperiodic Systemsp. 233
Introductionp. 233
Nonautonomous Hamiltonian systemsp. 235
Generalization of Yakubovich's theoremp. 238
Referencesp. 240
Longtime Dynamics in Adaptive Gain Control Systemsp. 241
Introductionp. 241
Assumptions and preliminariesp. 242
Localization of the global attractorp. 245
Longtime behavior and estimates of the Hausdorff dimension of the global attractorp. 248
Referencesp. 253
Model Reduction for Systems with Low-Dimensional Chaosp. 255
Introductionp. 255
Peak-to-peak dynamicsp. 256
The control problemp. 260
Examples of applicationp. 261
Delay-differential systemsp. 263
Concluding remarksp. 265
Referencesp. 267
Feedback Equivalence to Feedforward Forms for Nonlinear Single-Input Control Systemsp. 269
Introductionp. 269
Definitions and notationsp. 271
Feedforward normal formp. 274
m-invariantsp. 275
Main resultsp. 276
Examplesp. 281
Feedforward systems in E4p. 283
Referencesp. 285
Conservation Laws in Optimal Controlp. 287
Introductionp. 287
Preliminariesp. 289
Main resultsp. 291
Examplesp. 294
Referencesp. 295
List of Participantsp. 297
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9783540428909
ISBN-10: 3540428909
Series: Lecture Notes in Control and Information Sciences
Audience: General
Format: Paperback
Language: English
Number Of Pages: 304
Published: 11th January 2002
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 23.39 x 15.6  x 1.68
Weight (kg): 0.45