Algebraic Methods for Nonlinear Control Systems (eBook)

Giuseppe Conte, Claude H. Moog, Anna Maria Perdon (Autoren)

eBook Download: PDF

2007 | 2nd ed. 2007
XVI, 178 Seiten
Springer London (Verlag)
978-1-84628-595-0 (ISBN)

Infos

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.

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A self-contained introduction to algebraic control for nonlinear systems suitable for researchers and graduate students. "e;Algebraic Methods for Nonlinear Control Systems"e; develops a linear-algebraic alternative to the usual differential-geometric approach to nonlinear control, using vector spaces over suitable fields of nonlinear functions. It describes a range of results, some of which can be derived using differential geometry but many of which cannot. They include: classical and generalized realization in the nonlinear context; accessibility and observability recast for the linear-algebraic setting; discussion and solution of basic feedback problems; results for dynamic and static state and output feedback. Dynamic feedback and realization are shown to be dealt with and solved much more easily in the algebraic framework. The second edition has been completely revised with new text, examples and exercises; it is divided into two parts: necessary methodology and applications to control problems.

Inhalt

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

Produkt-Details

• Erscheint lt. Verlag: 19.1.2007
• Reihe/Serie: Communications and Control Engineering
• Zusatzinfo: XVI, 178 p.
• Verlagsort: London
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Informatik ► Theorie / Studium
• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Themenwelt: Naturwissenschaften
• Themenwelt: Technik ► Bauwesen
• Themenwelt: Technik ► Elektrotechnik / Energietechnik
• Themenwelt: Technik ► Maschinenbau
• Schlagworte: Complexity • Control • Control Theory • Dynamic State Feedback • linear algebra • matrix theory • Modeling • Nonlinear Control • nonlinear control system • nonlinear system • Nonlinear Systems • Systems Theory
• ISBN-10: 1-84628-595-X / 184628595X
• ISBN-13: 978-1-84628-595-0 / 9781846285950