Cooperative control of dynamical systems : applications to autonomous vehicles / Zhihua Qu.

Format:

Book

Author/Creator:

Qu, Zhihua, 1963-

Contributor:

Louis A. Duhring Fund.

Language:

English

Subjects (All):

Motor vehicles--Dynamics.

Motor vehicles.

Physical Description:

xvi, 325 pages : illustrations (some color) ; 25 cm

Place of Publication:

London : Springer, [2009]

Summary:

Whether providing automated passenger transport systems, exploring the hostile depths of the ocean or assisting soldiers in battle, autonomous vehicle systems are becoming an important fact of modern life. Distributed sensing and communication networks allow neighboring vehicles to share information autonomously, to interact with an operator, and to coordinate their motion to exhibit certain cooperative behaviors. The less structured the operating environment and the more changes the vehicle network experiences, the more difficult to grapple with problems of control become.

Cooperative Control of Dynamical Systems begins with a concise overview of cooperative behaviors and the modeling of constrained non-linear dynamical systems like ground, aerial, and underwater vehicles. A review of useful concepts from system theory is included. New results on cooperative control of linear and non-linear systems and on control of individual non-holonomic systems are presented. Control design in autonomous-vehicle applications moves evenly from open-loop steering control and feedback stabilization of an individual vehicle to cooperative control of multiple vehicles. This progression culminates in a decentralized control hierarchy requiring only local feedback information.

A number of novel methods are presented: parameterization for collision avoidance and real-time optimization in path planning; near optimal tracking and regulation control of non-holonomic chained systems; the matrix-theoretical approach to cooperative stability analysis of linear networked systems; the comparative argument of Lyapunov function components for analyzing non-linear cooperative systems; and cooperative control designs. These methods are used to generate solutions of guaranteed performance for the fundamental problems of:

optimized collision-free path planning;

near-optimal stabilization of non-holonomic systems; and

cooperative control of heterogeneous dynamical systems, including non-holonomic systems.

Examples, simulations and comparative studies bring immediacy to the fundamental issues while illustrating the theoretical foundations and the technical approaches and verifying the performance of the final control designs.

Researchers studying non-linear systems, control of networked systems, or mobile robot systems will find the wealth of new methods and solutions laid out in this book to be of great interest to their work. Engineers designing and building autonomous vehicles will also benefit from these ideas, and students will find this a valuable reference.

Contents:

1 Introduction 1

1.1 Cooperative, Pliable and Robust Systems 1

1.1.1 Control Through an Intermittent Network 2

1.1.2 Cooperative Behaviors 4

1.1.3 Pliable and Robust Systems 10

1.2 Modeling of Constrained Mechanical Systems 11

1.2.1 Motion Constraints 11

1.2.2 Kinematic Model 12

1.2.3 Dynamic Model 13

1.2.4 Hamiltonian and Energy 15

1.2.5 Reduced-order Model 15

1.2.6 Underactuated Systems 17

1.3 Vehicle Models 18

1.3.1 Differential-drive Vehicle 18

1.3.2 A Car-like Vehicle 20

1.3.3 Tractor-trailer Systems 23

1.3.4 A Planar Space Robot 25

1.3.5 Newton's Model of Rigid-body Motion 26

1.3.6 Underwater Vehicle and Surface Vessel 29

1.3.7 Aerial Vehicles 31

1.3.8 Other Models 34

1.4 Control of Heterogeneous Vehicles 34

1.5 Notes and Summary 37

2 Preliminaries on Systems Theory 39

2.1 Matrix Algebra 39

2.2 Useful Theorems and Lemma 43

2.2.1 Contraction Mapping Theorem 43

2.2.2 Barbalat Lemma 44

2.2.3 Comparison Theorem 45

2.3 Lyapunov Stability Analysis 48

2.3.1 Lyapunov Direct Method 51

2.3.2 Explanations and Enhancements 54

2.3.3 Control Lyapunov Function 58

2.3.4 Lyapunov Analysis of Switching Systems 59

2.4 Stability Analysis of Linear Systems 62

2.4.1 Eigenvalue Analysis of Linear Time-invariant Systems 62

2.4.2 Stability of Linear Time-varying Systems 63

2.4.3 Lyapunov Analysis of Linear Systems 66

2.5 Controllability 69

2.6 Non-linear Design Approaches 73

2.6.1 Recursive Design 73

2.6.2 Feedback Linearization 75

2.6.3 Optimal Control 77

2.6.4 Inverse Optimality and Lyapunov Function 78

2.7 Notes and Summary 79

3 Control of Non-holonomic Systems 81

3.1 Canonical Form and Its Properties 81

3.1.1 Chained Form 82

3.1.2 Controllability 85

3.1.3 Feedback Linearization 87

3.1.4 Options of Control Design 90

3.1.5 Uniform Complete Controllability 92

3.1.6 Equivalence and Extension of Chained Form 96

3.2 Steering Control and Real-time Trajectory Planning 98

3.2.1 Navigation of Chained Systems 98

3.2.2 Path Planning in a Dynamic Environment 104

3.2.3 A Real-time and Optimized Path Planning Algorithm 109

3.3 Feedback Control of Non-holonomic Systems 116

3.3.1 Tracking Control Design 118

3.3.2 Quadratic Lyapunov Designs of Feedback Control 120

3.3.3 Other Feedback Designs 128

3.4 Control of Vehicle Systems 130

3.4.1 Formation Control 131

3.4.2 Multi-objective Reactive Control 136

3.5 Notes and Summary 147

4 Matrix Theory for Cooperative Systems 153

4.1 Non-negative Matrices and Their Properties 153

4.1.1 Reducible and Irreducible Matrices 154

4.1.2 Perron-Frobenius Theorem 155

4.1.3 Cyclic and Primitive Matrices 158

4.2 Importance of Non-negative Matrices 161

4.2.1 Geometrical Representation of Non-negative Matrices 165

4.2.2 Graphical Representation of Non-negative Matrices 166

4.3 M-matrices and Their Properties 167

4.3.1 Diagonal Dominance 167

4.3.2 Non-singular M-matrices 168

4.3.3 Singular M-matrices 170

4.3.4 Irreducible M-matrices 172

4.3.5 Diagonal Lyapunov Matrix 174

4.3.6 A Class of Interconnected Systems 176

4.4 Multiplicative Sequence of Row-stochastic Matrices 177

4.4.1 Convergence of Power Sequence 178

4.4.2 Convergence Measures 179

4.4.3 Sufficient Conditions on Convergence 187

4.4.4 Necessary and Sufficient Condition on Convergence 188

4.5 Notes and Summary 192

5 Cooperative Control of Linear Systems 195

5.1 Linear Cooperative System 195

5.1.1 Characteristics of Cooperative Systems 196

5.1.2 Cooperative Stability 198

5.1.3 A Simple Cooperative System 200

5.2 Linear Cooperative Control Design 201

5.2.1 Matrix of Sensing and Communication Network 202

5.2.2 Linear Cooperative Control 203

5.2.3 Conditions of Cooperative Controllability 206

5.2.4 Discrete Cooperative System 209

5.3 Applications of Cooperative Control 210

5.3.1 Consensus Problem 210

5.3.2 Rendezvous Problem and Vector Consensus 212

5.3.3 Hands-off Operator and Virtual Leader 212

5.3.4 Formation Control 216

5.3.5 Synchronization and Stabilization of Dynamical Systems 222

5.4 Ensuring Network Connectivity 223

5.5 Average System and Its Properties 226

5.6 Cooperative Control Lyapunov Function 229

5.6.1 Fixed Topology 230

5.6.2 Varying Topologies 237

5.7 Robustness of Cooperative Systems 238

5.8 Integral Cooperative Control Design 248

5.9 Notes and Summary 251

6 Cooperative Control of Non-linear Systems 253

6.1 Networked Systems with Balanced Topologies 254

6.2 Networked Systems of Arbitrary Topologies 256

6.2.1 A Topology-based Comparison Theorem 256

6.2.2 Generalization 263

6.3 Cooperative Control Design 266

6.3.1 Systems of Relative Degree One 267

6.3.2 Systems in the Feedback Form 270

6.3.3 Affine Systems 274

6.3.4 Non-affine Systems 275

6.3.5 Output Cooperation 277

6.4 Discrete Systems and Algorithms 278

6.5 Driftless Non-holonomic Systems 281

6.5.1 Output Rendezvous 281

6.5.2 Vector Consensus During Constant Line Motion 285

6.6 Robust Cooperative Behaviors 288

6.6.1 Delayed Sensing and Communication 290

6.6.2 Vehicle Cooperation in a Dynamic Environment 294

6.7 Notes and Summary 296.

Notes:

Includes bibliographical references and index.

Local Notes:

Acquired for the Penn Libraries with assistance from the Louis A. Duhring Fund.

ISBN:

184882324X

9781848823242

OCLC:

305125631

Publisher Number:

99934680148