Analysis and Design of Nonlinear Control Systems

by Cheng, Daizhan; Hu, Xiaoming; Shen, Tielong

• ISBN13: 9783642115493
• ISBN10: 3642115497
• Format: Hardcover
• Copyright: 2011-05-29
• Publisher: Springer Verlag

Summary

"Analysis and Design of Nonlinear Control Systems" provides a comprehensive and up to date introduction to nonlinear control systems, including system analysis and major control design techniques. The book is self-contained, providing sufficient mathematical foundations for understanding the contents of each chapter. Scientists and engineers engaged in the field of Nonlinear Control Systems will find it an extremely useful handy reference book.Dr. Daizhan Cheng, a professor at Institute of Systems Science, Chinese Academy of Sciences, has been working on the control of nonlinear systems for over 30 years and is currently a Fellow of IEEE and a Fellow of IFAC, he is also the chairman of Technical Committee on Control Theory, Chinese Association of Automation.

Author Biography

Dr. Daizhan Cheng, a professor at Institute of Systems Science, Chinese Academy of Sciences, has been working on the control of nonlinear systems for over 30 years and is currently a Fellow of IEEE and a Fellow of IFAC, he is also the chairman of Technical Committee on Control Theory, Chinese Association of Automation.

Table of Contents

Introduction	p. 1
Linear Control Systems	p. 1
Controllability, Observability	p. 3
Invariant Subspaces	p. 6
Zeros, Poles, Observers	p. 8
Normal Form and Zero Dynamics	p. 10
Nonlinearity vs. Linearity	p. 14
Localization	p. 14
Singularity	p. 16
Complex Behaviors	p. 18
Some Examples of Nonlinear Control Systems	p. 20
References	p. 27
Topological Space	p. 29
Metric Space	p. 29
Topological Spaces	p. 34
Continuous Mapping	p. 39
Quotient Spaces	p. 44
References	p. 46
Differentiable Manifold	p. 47
Structure of Manifolds	p. 47
Fiber Bundle	p. 53
Vector Field	p. 56
One Parameter Group	p. 60
Lie Algebra of Vector Fields	p. 62
Co-tangent Space	p. 65
Lie Derivatives	p. 66
Frobenius' Theory	p. 70
Lie Series, Chow's Theorem	p. 72
Tensor Field	p. 75
Riemannian Geometry	p. 79
Symplectic Geometry	p. 85
References	p. 89
Algebra, Lie Group and Lie Algebra	p. 91
Group	p. 91
Ring and Algebra	p. 97
Homotopy	p. 100
Fundamental Group	p. 101
Covering Space	p. 109
Lie Group	p. 113
Lie Algebra of Lie Group	p. 115
Structure of Lie Algebra	p. 117
References	p. 119
Controllability and Observability	p. 121
Controllability of Nonlinear Systems	p. 121
Observability of Nonlinear Systems	p. 136
Kalman Decomposition	p. 140
References	p. 145
Global Controllability of Affine Control Systems	p. 147
From Linear to Nonlinear Systems	p. 147
A Sufficient Condition	p. 150
Multi-hierarchy Case	p. 163
Codim(g) = 1	p. 168
References	p. 171
Stability and Stabilization	p. 173
Stability of Dynamic Systems	p. 173
Stability in the Linear Approximation	p. 175
The Direct Method of Lyapunov	p. 177
Positive Definite Functions	p. 177
Critical Stability	p. 179
Instability	p. 180
Asymptotic Stability	p. 180
Total Stability	p. 182
Global Stability	p. 182
LaSalle's Invariance Principle	p. 183
Converse Theorems to Lyapunov's Stability Theorems	p. 185
Converse Theorems to Local Asymptotic Stability	p. 185
Converse Theorem to Global Asymptotic Stability	p. 187
Stability of Invariant Set	p. 188
Input-Output Stability	p. 189
Stability of Input-Output Mapping	p. 190
The Lur'e Problem	p. 192
Control Lyapunov Function	p. 193
Region of Attraction	p. 194
References	p. 205
Decoupling	p. 207
(f,g)-invariant Distribution	p. 207
Local Disturbance Decoupling	p. 213
Controlled Invariant Distribution	p. 218
Block Decomposition	p. 223
Feedback Decomposition	p. 232
References	p. 235
Input-Output Structure	p. 237
Decoupling Matrix	p. 237
Morgan's Problem	p. 240
Invertibility	p. 243
Decoupling via Dynamic Feedback	p. 247
Normal Form of Nonlinear Control Systems	p. 253
Generalized Normal Form	p. 256
Fliess Functional Expansion	p. 264
Tracking via Fliess Functional Expansion	p. 267
References	p. 277
Linearization of Nonlinear Systems	p. 279
Poincaré Linearization	p. 279
Linear Equivalence of Nonlinear Systems	p. 282
State Feedback Linearization	p. 287
Linearization with Outputs	p. 292
Global Linearization	p. 295
Non-regular Feedback Linearization	p. 306
References	p. 313
Design of Center Manifold	p. 315
Center Manifold	p. 315
Stabilization of Minimum Phase Systems	p. 317
Lyapunov Function with Homogeneous Derivative	p. 319
Stabilization of Systems with Zero Center	p. 328
Stabilization of Systems with Oscillatory Center	p. 335
Stabilization Using Generalized Normal Form	p. 341
Advanced Design Techniques	p. 349
References	p. 353
Output Regulation	p. 355
Output Regulation of Linear Systems	p. 355
Nonlinear Local Output Regulation	p. 366
Robust Local Output Regulation	p. 374
References	p. 377
Dissipative Systems	p. 379
Dissipative Systems	p. 379
Passivity Conditions	p. 383
Passivity-based Control	p. 388
Lagrange Systems	p. 393
Hamiltonian Systems	p. 397
References	p. 401
L2-Gain Synthesis	p. 403
H∞ Norm and L2-Gain	p. 403
H∞ Feedback Control Problem	p. 409
L2-Gain Feedback Synthesis	p. 411
Constructive Design Method	p. 417
Applications	p. 423
References	p. 429
Switched Systems	p. 431
Common Quadratic Lyapunov Function	p. 431
Quadratic Stabilization of Planar Switched Systems	p. 454
Controllability of Switched Linear Systems	p. 467
Controllability of Switched Bilinear Systems	p. 476
LaSalle's Invariance Principle for Switched Systems	p. 483
Consensus of Multi-Agent Systems	p. 492
Two Dimensional Agent Model with a Leader	p. 493
n Dimensional Agent Model without Lead	p. 495
References	p. 508
Discontinuous Dynamical Systems	p. 509
Introduction	p. 509
Filippov Framework	p. 510
Filippov Solution	p. 510
Lyapunov Stability Criteria	p. 513
Feedback Stabilization	p. 517
Feedback Controller Design: Nominal Case	p. 518
Robust Stabilization	p. 521
Design Example of Mechanical Systems	p. 523
PD Controlled Mechanical Systems	p. 523
Stationary Set	p. 524
Application Example	p. 528
References	p. 531
Some Useful Theorems	p. 533
Sard's Theorem	p. 533
Rank Theorem	p. 533
References	p. 533
Semi-Tensor Product of Matrices	p. 535
A Generalized Matrix Product	p. 535
Swap Matrix	p. 537
Some Properties of Semi-Tensor Product	p. 538
Matrix Form of Polynomials	p. 539
References	p. 540
Index	p. 541
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