Algebraic methods for nonlinear control systems

✍ Scribed by Giuseppe Conte, Claude H. Moog, Anna Maria Perdon

• Publisher: Springer
• Year: 2007
• Tongue: English
• Leaves: 183
• Series: Communications and Control Engineering
• Edition: 2ed.
• Category: Library

✦ Synopsis

This is a self-contained introduction to algebraic control for nonlinear systems suitable for researchers and graduate students. It is the first book dealing with the linear-algebraic approach to nonlinear control systems in such a detailed and extensive fashion. It provides a complementary approach to the more traditional differential geometry and deals more easily with several important characteristics of nonlinear systems.

✦ Table of Contents

Contents......Page 11
Part I: Methodology......Page 15
1. Preliminaries......Page 16
1.1 Analytic and Meromorphic Functions......Page 17
1.2 Control Systems......Page 21
1.3 Linear Algebraic Setting......Page 23
1.4 Frobenius Theorem......Page 27
1.5 Examples......Page 29
Problems......Page 31
2.1 State Elimination......Page 33
2.2 Examples......Page 37
2.3 Generalized Realization......Page 38
2.4 Classical Realization......Page 40
2.5 Input-output Equivalence and Realizations......Page 41
2.6 A Necessary and Sufficient Condition for the Existence of a Realization......Page 43
2.7 Minimal Realizations......Page 45
2.8 Affine Realizations......Page 46
2.9 The Hopping Robot......Page 51
2.10 Some Models......Page 53
Problems......Page 54
3.2 Examples......Page 56
3.3 Reachability, Controllability, and Accessibility......Page 57
3.4 Autonomous Elements......Page 58
3.5 Accessible Systems......Page 60
3.6 Controllability Canonical Form......Page 61
3.7 Controllability Indices......Page 62
Problems......Page 64
4.2 Examples......Page 66
4.3 Observability......Page 67
4.4 The Observable Space......Page 68
4.5 Observability Canonical Form......Page 71
4.6 Observability Indices......Page 72
4.7 Synthesis of Observers......Page 73
Problems......Page 80
5.1 Introductory Examples......Page 81
5.2 Inverse Systems......Page 82
5.3 Structural Indices......Page 83
5.4 Structure Algorithm......Page 86
5.5 Invertibility......Page 93
5.6 Zero Dynamics......Page 94
Problems......Page 97
6.1 Generalized State-space Transformation......Page 99
6.2 Regular Generalized State Feedback......Page 100
6.3 Generalized Output Injection......Page 102
6.4 Canonical Form......Page 103
6.5 Generalizing the Notion of Output Injection......Page 109
Problem......Page 112
Part II: Applications to Control Problems......Page 113
7.1 Input-output Linearization Problem Statement......Page 114
7.3 Multioutput Case......Page 115
7.4 Trajectory Tracking......Page 118
Problems......Page 122
8.1 Noninteracting Control Problem Statement......Page 123
8.3 Dynamic State Feedback Solution......Page 124
8.4 Noninteracting Control via Quasi-static State Feedback......Page 125
Problem......Page 126
9.1 Input-state Linearization Problem Statement......Page 127
9.2 Static State Feedback Solution......Page 128
9.3 Partial Linearization......Page 130
Problem......Page 134
10. Disturbance Decoupling......Page 135
10.1 Solution of the Disturbance Decoupling Problem......Page 136
11.1 A Special Form of the Inversion Algorithm......Page 138
11.2 Model Matching Problem......Page 141
11.3 Left Factorization......Page 149
12.1 Input-output Linearization......Page 156
12.2 Input-output Decoupling......Page 171
Problem......Page 172
C......Page 173
D......Page 174
F......Page 175
H......Page 176
J......Page 177
M......Page 178
R......Page 179
Z......Page 180
O......Page 182
Z......Page 183