Dynamics Bifurcations and Control 1st Edition by Fritz Colonius, Lars Grune ISBN 9783540428909 by Fritz Colonius, Lars Grüne 9783540428909, 3540428909 instant download after payment.

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ISBN 13: 9783540428909
Author: Fritz Colonius, Lars Grune

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.

Dynamics Bifurcations and Control 1st Table of contents:

1. Controlling an Inverted Pendulum with Bounded Controls
2. Introduction
3. Description of the system
4. Bounded control law
5. Equilibrium points
6. Stability of the equilibria x00
7. Stability of the remaining equilibria
8. Local nonlinear analysis
9. Hopf bifurcation at the equilibrium point x00
10. Hopf bifurcation at the equilibrium points
11. Numerical analysis of the global dynamical behavior
12. Desired operating behaviour
13. Conclusions
14. Bifurcations of Neural Networks with Almost Symmetric Interconnection Matrices
15. Introduction
16. Neural network model and preliminaries
17. Limit cycles in a competivite neural network
18. Hopf bifurcations in sigmoidal neural networks
19. Period-doubling bifurcation in a third-order neural network
20. Conclusions
21. References
22. Bifurcations in Systems with a Rate Limiter
23. Introduction
24. Behaviour of rate limiters
25. Describing function of rate limiters
26. Limit cycle analysis of systems with rate limiters
27. Bifurcations in systems with a rate limiter
28. Saddle-node bifurcation of periodic orbits
29. Subcritical Hopf bifurcation at infinity
30. Supercritical Hopf-like bifurcation
31. Conclusions
32. Acknowledgments
33. References
34. Monitoring and Control of Bifurcations Using Probe Signals
35. Introduction
36. Hopf bifurcation
37. Analysis of the effects of near-resonant forcing
38. Averaged model
39. Calculation of shift in the critical value of the bifurcation parameter
40. Numerical example
41. Combined Stability Monitoring and Control
42. Detection of Impending Bifurcation in a Power System Model
43. Conclusions
44. Acknowledgments
45. References
46. Normal From, Invariants, and Bifurcations of Nonlinear Control Systems in the Particle Deflection Pl
47. Introduction
48. Problem formulation
49. Normal form and invariants
50. Normal form
51. Invariants
52. Resonant terms
53. Bifurcation of control systems
54. Systems with a double-zero uncontrollable mode
55. Systems with single-zero uncontrollable modes
56. Bifurcation control using state feedback
57. Bifurcations with quadratic degeneracy
58. Bifurcation with cubic degeneracy
59. The cusp bifurcation and hysteresis
60. Other related issues
61. Conclusions
62. References
63. Bifurcations of Reachable Sets Near an Abnormal Direction and Consequences
64. Setup and definitions
65. Abnormal trajectories
66. Accessibility sets
67. Single-input affine systems
68. Asymptotics of the reachable sets
69. Applications
70. Application to the optimality status of an abnormal trajectory
71. Application to the sub-Riemannian case
72. Oscillation Control in Delayed Feedback Systems
73. Introduction
74. Perturbations of linear retarded equations
75. The harmonic oscillator under delayed feedback
76. The linear equation
77. The reduced equation and averaging
78. Controlling the amplitude and frequency of oscillations
79. Conclusion
80. Nonlinear Problems in Friction Compensation
81. Introduction
82. Conic analysis of uncertain friction
83. Harmonic balance
84. Frequencial synthesis using QFT
85. Discussion
86. Acknowledgements
87. References
88. Time-Optimal Stabilization for a Third-Order Integrator: a Robust State-Feedback Implementation
89. Introduction
90. Closed loop time-optimal stabilization for a third-order integrator
91. Sliding-mode implementation of the time-optimal controller
92. Simulation results
93. Conclusions
94. Acknowledgements
95. References
96. Stability Analysis of Periodic Solutions via Integral Quadratic Constraints
97. Introduction
98. A motivating example
99. Problem formulation and preliminary results
100. Sufficient conditions for stability of periodic solutions
101. Application example
102. Conclusions
103. References
104. Port Controller Hamiltonian Synthesis Using Evolution Strategies
105. Introduction
106. Port controlled Hamiltonian systems
107. Controller design
108. Preliminaries on evolution strategies
109. Evolutionary basics
110. Fitness evaluation
111. Evolutionary formulation
112. Case study - ball & beam system
113. Conclusions
114. Acknowledgements
115. References
116. Feedback Stabilization and H∞ Control of Nonlinear Systems Affected by Disturbances: the Different
117. Introduction
118. Differential games approach to nonlinear H∞ control
119. Other stability questions
120. Building a feedback solution for nonlinear H∞ control
121. References
122. A Linearization Principle for Robustness with Respect to Time-Varying Perturbations*
123. Introduction
124. Preliminaries
125. The discrete time case
126. Continuous time
127. Conclusion
128. References
129. On Constrained Dynamical Systems and Algebroids
130. Introduction: Constrained Hamiltonian systems
131. What is a Lie algebroid?
132. Generalities
133. The algebroid structure of an integrable subbundle of a tangent bundle
134. Dirac structures and Port Controlled Hamiltonian systems
135. Dirac structures
136. Dynamics on Dirac structures
137. Application: Mechanical system with constraints
138. Port controlled Hamiltonian systems
139. Constrained mechanical systems and algebroids
140. Control of constrained mechanical systems
141. Acknowledgements
142. References
143. On the Classification of Control Sets
144. Introduction
145. Basic definition
146. Strong inner pairs
147. The dynamic index
148. The index of a control set near a periodic orbit
149. References
150. On the Frequency Theorem for Nonperiodic Systems
151. Introduction
152. Nonautonomous Hamiltonian systems
153. Generalization of Yakubovich's theorem
154. References
155. Longtime Dynamics in Adaptive Gain Control Systems
156. Introduction
157. Assumptions and preliminaries
158. Localization of the global attractor
159. Longtime behavior and estimates of the Hausdor dimension of the global attractor
160. Acknowledgment
161. References
162. Model Reduction for Systems with Low-Dimensional Chaos
163. Introduction
164. Peak-to-peak dynamics
165. The control problem
166. Examples of application
167. Lorenz system
168. Chua system
169. Delay-differential systems
170. Concluding remarks
171. References
172. Feedback Equivalence to Feedforward Forms for Nonlinear Single-Input Systems
173. Introduction
174. Definitions and notations
175. Feedforward normal form
176. m-inveriants
177. Main results
178. Feedforwads form: first nonlinearizable term
179. Feedforward form: the general step
180. Strict feedforward form
181. Nice feedforward form
182. Examples
183. Feedforward systems in R4
184. References
185. Conservation Laws in Optimal Control*
186. Introduction
187. Preliminaries
188. The Lagrange Problem of Optimal Control
189. The Maximum Principle
190. Mail results
191. A Necessary and Sufficient Condition
192. Noether Theorem for Optimal Control

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