Swarm Stability and Optimization (eBook)

Title 1
Preface 5
Contents 10
Part I Basic Principles 15
Introduction 16
Swarms in Biology and Engineering 16
For Further Reading 22
Early Works in Biology 22
Early Works in Physics 24
Early Works in Engineering and Computer Science 25
Swarm Coordination and Control Problems 28
Aggregation 28
Social Foraging 30
Formation Control and Swarm Tracking 31
Distributed Agreement 33
Function Minimization 35
Related Problems and Behaviors and Further Reading 36
Formation Structure Breakdowns 36
Flocking 36
Rendezvous 37
Synchronization of Coupled Nonlinear Oscillators 37
Other Behaviors 38
Part II Continuous Time Swarms 39
Swarms of Single Integrator Agents 40
Single Integrator Agent Model 40
Aggregation 41
Potential Function Design 41
Analysis of Swarm Motion 43
Swarm Cohesion Analysis 46
Agents with Finite Body Size 52
Simulation Examples 55
Social Foraging 57
Introduction 57
Swarm Cohesion Analysis 59
Swarm Motion in Various Resource Profiles 62
Analysis of Individual Behavior in a Cohesive Swarm 70
Simulation Examples 71
Formation Control 75
Simulation Examples 77
Swarm Tracking 78
Simulation Examples 82
Further Issues 83
General Neighborhood Topology 83
Non-reciprocal Agent Interactions 84
For Further Reading 84
Swarms of Double Integrator Agents 85
Double Integrator Model 85
Stability Analysis of Swarm Cohesion Properties 86
Controls and Error Dynamics 87
Cohesive Social Foraging with Noise 91
Special Case: Identical Agents 103
Stability Analysis of Swarm Trajectory Following 109
Simulation Examples 112
No-Noise Case 112
Noise Case 112
Further Issues 115
Extensions and Generalizations 115
For Further Reading 115
Swarms of Fully Actuated Agents with Model Uncertainty 116
Fully Actuated Agent Model with Uncertainty 116
Controller Development 117
Aggregation, Foraging, and Formation Control 117
Swarm Tracking 120
Potential Functions and Bounds 123
Aggregation 123
Social Foraging 124
Formation Control 126
Swarm Tracking 126
Simulation Examples 127
Aggregation 128
Social Foraging 129
Formation Control 130
Swarm Tracking 131
Further Issues 132
Extensions and Generalizations 132
For Further Reading 132
Swarms of Non-holonomic Unicycle Agents with Model Uncertainty 133
Non-holonomic Unicycle Agent Model with Uncertainty 133
Controller Development 134
Aggregation, Foraging, and Formation Control 134
Swarm Tracking 139
Potential Functions and Bounds 142
Aggregation 142
Social Foraging 145
Formation Control 147
Swarm Tracking 147
Simulation Examples 149
Aggregation 150
Social Foraging 152
Formation Control 152
Swarm Tracking 153
Further Issues 154
Model Equivalence 154
Extensions and Generalizations 156
For Further Reading 156
Formation Control Using Nonlinear Servomechanism 158
General Non-linear Agent Model 158
Nonlinear Servomechanism Based Controller Development 161
Full Information Controller 162
Error Feedback Controller 163
Formation Reconfiguration 165
Expansion/Contraction 167
Rotation 167
Topology Change 168
Illustrative Examples 168
Further Issues 177
Extensions and Generalizations 177
For Further Reading 179
Part III Discrete Time Swarms 181
One-Dimensional Discrete-Time Swarm 182
The Swarm Model 182
Agent Model 182
One-Dimensional Swarm Model 183
The System under Total Synchronism 188
Asynchronous Swarm 194
Simulation Results 198
Further Issues 200
Extensions and Generalizations 200
For Further Reading 200
Asynchronous Distributed Agreement in Discrete Time Swarms 201
Model of the System 201
System under Total Synchronism 204
Asynchronous System 208
Simulation Examples 212
Further Issues 217
Application Areas of the Agreement Model 217
Extensions and Generalizations 218
For Further Reading 220
Formation Control with Potential Functions and Newton’s Iteration 222
Path Planning for a Single Agent 222
Controller Development 226
Simulation Examples 230
Further Issues 233
Extensions and Generalizations 233
For Further Reading 233
Part IV Swarm Based Optimization Methods 234
Bacteria Foraging Optimization 235
Bacterial Foraging by E. coli 235
Swimming and Tumbling 235
Chemotaxis and Climbing Nutrient Gradients 237
Underlying Sensing and Decision-Making Mechanisms 238
Elimination and Dispersal Events 239
E. coli Bacterial Foraging for Optimization 240
An Optimization Model for E. coli Bacterial Foraging 240
Bacterial Foraging Optimization Algorithm (BFOA) 244
Guidelines for Algorithm Parameter Choices 246
Relations to the Genetic Algorithm 247
Example: Function Optimization via E. coli Foraging 247
Nutrient Hill-Climbing: No Swarming 248
Swarming Effects 249
Further Issues 250
Extensions and Generalizations 251
For Further Reading 251
Particle Swarm Optimization 252
Basic PSO Iteration 252
Synchronous and Asynchronous PSO Implementations 254
Traditional PSO Implementations 254
Decentralized Asynchronous PSO Formulation 256
Particle Neighborhoods 258
Static Neighborhood 258
Dynamic Neighborhood 260
Directed Graph Representation of Particle Neighborhoods 265
Connectivity of the Swarm 267
Simulation Examples 271
Further Issues 276
Extensions and Generalizations 278
For Further Reading 279
References 281
Index 295