Analysis and Design of Nonlinear Control Systems

✍ Scribed by Daizhan Cheng, Xiaoming Hu, Tielong Shen

• Publisher: Springer
• Year: 2011
• Tongue: English
• Leaves: 560
• Edition: 1st Edition.
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Cover......Page 1
Analysis and Design of
Nonlinear Control
Systems......Page 4
ISBN 9783642115493......Page 5
Preface......Page 6
Table of Contents
......Page 10
Symbols......Page 14
1.1 Linear Control Systems......Page 16
1.1.1 Controllability, Observability......Page 18
1.1.2 Invariant Subspaces......Page 21
1.1.3 Zeros, Poles, Observers......Page 23
1.1.4 Normal Form and Zero Dynamics......Page 25
1.2.1 Localization......Page 29
1.2.2 Singularity......Page 31
1.2.3 Complex Behaviors......Page 33
1.3 Some Examples of Nonlinear Control Systems......Page 35
References......Page 42
2.1 Metric Space......Page 44
2.2 Topological Spaces......Page 49
2.3 Continuous Mapping......Page 54
2.4 Quotient Spaces......Page 59
References......Page 61
3.1 Structure of Manifolds......Page 62
3.2 Fiber Bundle......Page 68
3.3 Vector Field......Page 71
3.4 One Parameter Group......Page 75
3.5 Lie Algebra of Vector Fields......Page 77
3.6 Co-tangent Space......Page 80
3.7 Lie Derivatives......Page 81
3.8 Frobenius’ Theory......Page 85
3.9 Lie Series, Chow’s Theorem......Page 87
3.10 Tensor Field......Page 90
3.11 Riemannian Geometry......Page 94
3.12 Symplectic Geometry......Page 100
References......Page 104
4.1 Group......Page 106
4.2 Ring and Algebra......Page 112
4.3 Homotopy......Page 115
4.4 Fundamental Group......Page 116
4.5 Covering Space......Page 124
4.6 Lie Group......Page 128
4.7 Lie Algebra of Lie Group......Page 130
4.8 Structure of Lie Algebra......Page 132
References......Page 134
5.1 Controllability of Nonlinear Systems......Page 136
5.2 Observability of Nonlinear Systems......Page 151
5.3 Kalman Decomposition......Page 155
References......Page 160
6.1 From Linear to Nonlinear Systems......Page 162
6.2 A Sufficient Condition......Page 165
6.3 Multi-hierarchy Case......Page 178
6.4 Codim(G) = 1......Page 183
References......Page 186
7.1 Stability of Dynamic Systems......Page 188
7.2 Stability in the Linear Approximation......Page 190
7.3.1 Positive Definite Functions......Page 192
7.3.2 Critical Stability......Page 194
7.3.4 Asymptotic Stability......Page 195
7.3.6 Global Stability......Page 197
7.4 LaSalle’s Invariance Principle......Page 198
7.5.1 Converse Theorems to Local Asymptotic Stability......Page 200
7.5.2 Converse Theorem to Global Asymptotic Stability......Page 202
7.6 Stability of Invariant Set......Page 203
7.7 Input-Output Stability......Page 204
7.7.1 Stability of Input-Output Mapping......Page 205
7.7.2 The Lur’e Problem......Page 207
7.7.3 Control Lyapunov Function......Page 208
7.8 Region of Attraction......Page 209
References......Page 220
8.1 ( f,g)-invariant Distribution......Page 222
8.2 Local Disturbance Decoupling......Page 228
8.3 Controlled Invariant Distribution......Page 233
8.4 Block Decomposition......Page 238
8.5 Feedback Decomposition......Page 247
References......Page 250
9.1 DecouplingMatrix......Page 252
9.2 Morgan’s Problem......Page 255
9.3 Invertibility......Page 258
9.4 Decoupling via Dynamic Feedback......Page 262
9.5 Normal Form of Nonlinear Control Systems......Page 268
9.6 Generalized Normal Form......Page 271
9.7 Fliess Functional Expansion......Page 279
9.8 Tracking via Fliess Functional Expansion......Page 282
References......Page 292
10.1 Poincare´ Linearization......Page 294
10.2 Linear Equivalence of Nonlinear Systems......Page 297
10.3 State Feedback Linearization......Page 302
10.4 Linearization with Outputs......Page 307
10.5 Global Linearization......Page 310
10.6 Non-regular Feedback Linearization......Page 321
References......Page 328
11.1 Center Manifold......Page 330
11.2 Stabilization of Minimum Phase Systems......Page 332
11.3 Lyapunov Function with Homogeneous Derivative......Page 334
11.4 Stabilization of Systems with Zero Center......Page 343
11.5 Stabilization of Systems with Oscillatory Center......Page 350
11.6 Stabilization Using Generalized Normal Form......Page 356
11.7 Advanced Design Techniques......Page 364
References......Page 368
12.1 Output Regulation of Linear Systems......Page 370
12.2 Nonlinear Local Output Regulation......Page 381
12.3 Robust Local Output Regulation......Page 389
References......Page 392
13.1 Dissipative Systems......Page 394
13.2 Passivity Conditions......Page 398
13.3 Passivity-based Control......Page 403
13.4 Lagrange Systems......Page 408
13.5 Hamiltonian Systems......Page 412
References......Page 416
14.1 H Norm and L2-Gain......Page 418
14.2 H Feedback Control Problem......Page 424
14.3 L2-Gain Feedback Synthesis......Page 426
14.4 Constructive Design Method......Page 432
14.5 Applications......Page 438
References......Page 444
15.1 Common Quadratic Lyapunov Function......Page 446
15.2 Quadratic Stabilization of Planar Switched Systems......Page 469
15.3 Controllability of Switched Linear Systems......Page 482
15.4 Controllability of Switched Bilinear Systems......Page 491
15.5 LaSalle’s Invariance Principle for Switched Systems......Page 498
15.6 Consensus of Multi-Agent Systems......Page 507
15.6.1 Two Dimensional Agent Model with a Leader......Page 508
15.6.2 n Dimensional Agent Model without Lead......Page 510
References......Page 523
16.1 Introduction......Page 524
16.2.1 Filippov Solution......Page 525
16.2.2 Lyapunov Stability Criteria......Page 528
16.3 Feedback Stabilization......Page 532
16.3.1 Feedback Controller Design: Nominal Case......Page 533
16.3.2 Robust Stabilization......Page 536
16.4.1 PD Controlled Mechanical Systems......Page 538
16.4.2 Stationary Set......Page 539
16.4.3 Application Example......Page 543
References......Page 546
References......Page 548
B.1 A Generalized Matrix Product......Page 550
B.2 Swap Matrix......Page 552
B.3 Some Properties of Semi-Tensor Product......Page 553
B.4 Matrix Form of Polynomials......Page 554
References......Page 555
Index......Page 556