Algebraic Methods for Nonlinear Control Systems (eBook)

Preface to the Second Edition 7
Preface to the First Edition 8
Contents 11
Methodology 15
1 Preliminaries 16
1.1 Analytic and Meromorphic Functions 17
1.2 Control Systems 21
1.3 Linear Algebraic Setting 23
1.4 Frobenius Theorem 27
1.5 Examples 29
Problems 31
2 Modeling 33
2.1 State Elimination 33
2.2 Examples 37
2.3 Generalized Realization 38
2.4 Classical Realization 40
2.5 Input-output Equivalence and Realizations 41
2.6 A Necessary and Sufficient Condition for the Existence of a Realization 43
2.7 Minimal Realizations 45
2.8 Affine Realizations 46
2.9 The Hopping Robot 51
2.10 Some Models 53
Problems 54
3 Accessibility 56
3.1 Introduction 56
3.2 Examples 56
3.3 Reachability, Controllability, and Accessibility 57
3.4 Autonomous Elements 58
3.5 Accessible Systems 60
3.6 Controllability Canonical Form 61
3.7 Controllability Indices 62
3.8 Accessibility of the Hopping Robot Model 64
Problems 64
4 Observability 66
4.1 Introduction 66
4.2 Examples 66
4.3 Observability 67
4.4 The Observable Space 68
4.5 Observability Canonical Form 71
4.6 Observability Indices 72
4.7 Synthesis of Observers 73
Problems 80
5 Systems Structure and Inversion 81
5.1 Introductory Examples 81
5.2 Inverse Systems 82
5.3 Structural Indices 83
5.4 Structure Algorithm 86
5.5 Invertibility 93
5.6 Zero Dynamics 94
Problems 97
6 System Transformations 99
6.1 Generalized State-space Transformation 99
6.2 Regular Generalized State Feedback 100
6.3 Generalized Output Injection 102
6.4 Canonical Form 103
6.5 Generalizing the Notion of Output Injection 109
Problem 112
Applications to Control Problems 113
7 Input-output Linearization 114
7.1 Input-output Linearization Problem Statement 114
7.2 Single-output Case 115
7.3 Multioutput Case 115
7.4 Trajectory Tracking 118
Problems 122
8 Noninteracting Control 123
8.1 Noninteracting Control Problem Statement 123
8.2 Static State Feedback Solution 124
8.3 Dynamic State Feedback Solution 124
8.4 Noninteracting Control via Quasi-static State Feedback 125
Problem 126
9 Input-state Linearization 127
9.1 Input-state Linearization Problem Statement 127
9.2 Static State Feedback Solution 128
9.3 Partial Linearization 130
Problem 134
10 Disturbance Decoupling 135
10.1 Solution of the Disturbance Decoupling Problem 136
11 Model Matching 138
11.1 A Special Form of the Inversion Algorithm 138
11.2 Model Matching Problem 141
11.3 Left Factorization 149
12 Measured Output Feedback Control Problems 156
12.1 Input-output Linearization 156
12.2 Input-output Decoupling 171
Problem 172
References 173
Index 182