Dynamic Surface Control of Uncertain Nonlinear Systems

by Song, Bongsob; Hedrick, J. Karl

• ISBN13: 9780857296313
• ISBN10: 0857296310
• Format: Hardcover
• Copyright: 2011-05-25
• Publisher: Springer Verlag

Summary

Although the problem of nonlinear controller design is as old as that of linear controller design, the systematic design methods framed in response are more sparse. Given the range and complexity of nonlinear systems, effective new methods of control design are therefore of significant importance.Dynamic Surface Control of Uncertain Nonlinear Systems provides a theoretically rigorous and practical introduction to nonlinear control design. The convex optimization approach applied to good effect in linear systems is extended to the nonlinear case using the new dynamic surface control (DSC) algorithm developed by the authors. A variety of problems #xE2;#xAC;#x1C; DSC design, output feedback, input saturation and fault-tolerant control among them #xE2;#xAC;#x1C; are considered. The inclusion of applications material demonstrates the real significance of the DSC algorithm, which is robust and easy to use, for nonlinear systems with uncertainty in automotive and robotics.Written for the researcher and graduate student of nonlinear control theory, this book will provide the applied mathematician and engineer alike with a set of powerful tools for nonlinear control design. It will also be of interest to practitioners working with a mechatronic systems in aerospace, manufacturing and automotive and robotics, milieux.

Table of Contents

Theory
Introduction	p. 3
A Brief History of Dynamic Surface Control	p. 3
Sliding Mode Control	p. 4
Integrator Backstepping	p. 5
Mismatched Uncertainties	p. 5
Design Methodology	p. 5
Multiple Sliding Surface Control	p. 7
Dynamic Surface Control	p. 11
Motivating Example	p. 11
An LMI Approach	p. 13
Book Organization	p. 14
Origin of the Book	p. 16
Dynamic Surface Control	p. 19
Motivation	p. 19
Problem Statement	p. 21
Design Procedure	p. 23
Augmented Error Dynamics	p. 25
Quadratic Stabilization	p. 30
Nominal Error Dynamics	p. 31
Norm-Bounded Error Dynamics	p. 35
Diagonal Norm-Bounded Error Dynamics	p. 41
Ultimate and Quadratic Boundedness	p. 44
Robustness to Uncertain Nonlinear Systems	p. 57
Uncertain Lipschitz Systems	p. 57
Problem Statement	p. 57
Quadratic Stability and Tracking	p. 58
Dsc with Nonlinear Damping	p. 66
Problem Statement	p. 66
Stabilization and Quadratic Boundedness	p. 67
Input-Output Stability	p. 75
Observer-Based Dynamic Surface Control	p. 79
Nonlinear Observer Design	p. 80
Problem Statement	p. 80
Quadratic Stability of Observer	p. 81
Design of Observer Gain Matrix	p. 85
A Separation Principle	p. 91
Preliminary Design of Odsc	p. 91
Augmented Error Dynamics	p. 92
Separation Principle of Error Dynamics	p. 96
Quadratic Stabilization and Tracking	p. 97
Consideration of Uncertainty	p. 100
Redesign of Nonlinear Observer	p. 102
Design Procedure of Odsc	p. 103
Constrained Stabilization	p. 107
Problem Statement and Preliminaries	p. 107
Local Regulation and Regions of Attraction	p. 110
Robust Constrained Stabilization	p. 117
Multi-Input Multi-Output Mechanical Systems	p. 123
Fully-Actuated Mechanical System	p. 124
Synthesis of Dynamic Surface Control	p. 125
Error Dynamics	p. 125
Synthesis for Stabilization	p. 127
Synthesis for Quadratic Tracking	p. 136
Avoiding Cancelations	p. 141
Extension to Rigid Body Dynamics	p. 142
Decentralized Dynamic Surface Control	p. 144
Preliminary Design of Ddsc	p. 144
Augmented Error Dynamics	p. 145
Decentralized Stabilization	p. 147
Applications
Automated Vehicle Control	p. 155
Application to Longitudinal Vehicle Control	p. 158
Engine and Brake Control via Dsc	p. 158
Switched Closed Loop Error Dynamics	p. 160
Simultaneous Quadratic Boundedness	p. 162
Input-Output Stability	p. 167
Passive Fault Tolerant Control	p. 169
Problem Statement	p. 170
Error Dynamics for a Faulty Nonlinear System	p. 171
Fault Classification	p. 175
Fault Tolerant Control for Ahs	p. 183
Controller Reconfiguration	p. 185
Observer-Based Dsc	p. 186
Trajectory Reconfiguration	p. 187
Longitudinal Control for an Automated Transit Bus	p. 189
Longitudinal Control via Dsc	p. 189
Quadratic Tracking and Validation	p. 193
Active Fault Tolerant Control	p. 198
Error Dynamics for Faulty System	p. 199
Sensor Fault Handling	p. 201
Trajectory Reconfiguration for Longitudinal Control	p. 207
Biped Robot Control	p. 217
Hybrid Biped Model	p. 218
Trajectory Generation	p. 221
Motion Control for Ssp and Dsp	p. 224
Application of Dynamic Surface Control	p. 224
Augmented Error Dynamics	p. 225
Piecewise Quadratic Boundedness	p. 227
Simulation Results	p. 228
AppendixProofs	p. 233
Proof of Lemma 2.1	p. 233
Proof of Lemma 3.1	p. 235
Proof of Lemma 3.2	p. 238
Proof of Theorem 5.3	p. 241
References	p. 245
Index	p. 251
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