Page 206 - Autonomous Mobile Robots

5 Stabilization of

Nonholonomic

Systems

Alessandro Astolfi

CONTENTS

5.1 Introduction ............................................................ 192
5.2 Preliminaries and Definitions ......................................... 193
5.3 Discontinuous Stabilization ........................................... 197
5.3.1 Stabilization of Discontinuous Nonholonomic Systems .... 198
5.3.2 The σ Process ................................................. 203
5.3.3 The Issue of Asymptotic Stability ............................ 204
5.3.4 An Algorithm to Design Almost Stabilizers ................. 207
5.4 Chained Systems and Power Systems ................................ 208
5.5 Discontinuous Control of Chained Systems .......................... 209
5.5.1 An Example: A Car-Like Vehicle ............................ 210
5.5.2 Discussion ..................................................... 213
5.6 Robust Stabilization — Part I ......................................... 213
5.7 Robust Stabilization — Part II ........................................ 216
5.7.1 The Local Controller .......................................... 216
5.7.2 The Global Controller......................................... 217
5.7.3 Definition of the Hybrid Controller and Main Result ....... 218
5.7.4 Discussion ..................................................... 218
5.8 Robust Stabilitazion — Part III ....................................... 219
5.8.1 Robust Sampled-Data Control of Power Systems ........... 219
5.8.2 An Example: A Car-Like Vehicle Revisited ................. 220
5.8.3 Discussion ..................................................... 221
5.9 Conclusions ............................................................ 221
Acknowledgments ............................................................ 223
References .................................................................... 223
Biography ..................................................................... 226

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© 2006 by Taylor & Francis Group, LLC

FRANKL: “dk6033_c005” — 2006/3/31 — 16:42 — page 191 — #5