CONTROL AND DYNAMIC SYSTEMS
CONTENTS INTRODUCTION WHAT IS A MULTI-AGENT SYSTEM? MULTI-AGENT SYSTEMS IN THE REAL WORLD SENSOR NETWORK SYSTEMS BIOLOGY SWARM ROBOTICS COLLECTIVE BEHAVIORS UAVS HUMAN SOCIETY CONTROL OF MULTI-AGENT SYSTEMS: EMERGING TOPICS IN SYSTEMS AND CONTROL CONSENSUS CONTROL COVERAGE CONTROL FORMATION CONTROL CONTROLLABILITY OF NETWORKS MODEL PREDICTIVE CONTROL EVENT-TRIGGERED AND SPARSE CONTROL MULTI-AGENT SYSTEMS IN OTHER IMPORTANT RESEARCH FIELDS GRAPH SIGNAL PROCESSING MACHINE LEARNING DISTRIBUTED OPTIMIZATION BOOLEAN NETWORKS SWARM INTELLIGENCE SYNCHRONIZATION SUMMARY REFERENCES LINEAR ALGEBRA AND GRAPH THEORY WITH PYTHON BRIEF INTRODUCTION TO PYTHON AN OVERVIEW OF PYTHON PYTHON ENVIRONMENT HELLO WORLD NUMERICAL COMPUTATION WITH PYTHON LINEAR ALGEBRA NOTATION MATRIX RANK POSITIVE AND NON-NEGATIVE MATRICES EIGENVALUES JORDAN CANONICAL FORM AND SPECTRAL DECOMPOSITION SPECTRAL MAPPING THEOREM GERSHGORIN CIRCLE THEOREM PERRON–FROBENIUS THEORY DE?NITE MATRICES LINEAR SYSTEMS AND MATRIX EXPONENTIAL PYTHON CODES FOR LINEAR ALGEBRA PYTHON CODE 2 1: GERSHGORIN CIRCLES PYTHON CODE 2 2: ODE GRAPH THEORY WHAT IS A GRAPH? CONNECTIVITY SPANNING TREE GRAPH LAPLACIAN PERRON MATRICES GRAPH CONNECTIVITY ANALYSIS WITH GRAPH LAPLACIAN AND PERRON MATRICES GRAPH-RELATED DYNAMICAL SYSTEMS PYTHON CODES FOR GRAPH THEORY PYTHON CODE 2 3: GRAPH DRAWING PYTHON CODE 2 4: DIRECTED TREE PYTHON CODE 2 5: SPANNING TREE PYTHON CODE 2 6: ADJACENCY MATRIX PYTHON CODE 2 7: PERRON MATRIX OF A BALANCED GRAPH PYTHON CODE 2 8: GRAPH LAPLACIAN EXERCISES CONSENSUS PROBLEM CONSENSUS CONTROLLERS FOR INTEGRATOR AGENTS CONDITIONS FOR CONSENSUS DISCRETE-TIME CASE PERFORMANCE OF CONSENSUS CONTROLLERS PYTHON CODES PYTHON CODE 3 1: CONSENSUS CONTROL IN CONTINUOUS TIME PYTHON CODE 3 2: CONSENSUS CONTROL IN DISCRETE TIME COVERAGE PROBLEM VORONOI DIAGRAMS DE?NITION RELATION TO COVERAGE GRADIENT SYSTEMS COVERAGE CONTROLLERS FOR INTEGRATOR AGENTS PROOF OF THEOREM 4 1 APPLICATION TO MULTI-AGENT DISPLAY PYTHON CODE 4 1: COMPUTATION OF VORONOI DIAGRAM AND VORONOI CENTROIDS PYTHON CODE 4 2: COVERAGE CONTROL APPENDICES EXISTENCE OF UNIQUE SOLUTION TO NONLINEAR SYSTEMS LASALLE’S INVARIANCE PRINCIPLE DISTRIBUTED FORMATION CONTROL RIGIDITY THEORY DISTANCE RIGIDITY BEARING RIGIDITY WEAK RIGIDITY (ANGLE RIGIDITY) RIGIDITY-INDUCED FORMATION CONTROL DISTANCE-BASED FORMATION CONTROL BEARING-BASED FORMATION CONTROL ANGLE-BASED FORMATION CONTROL PYTHON CODE 5 1: DISTANCE-BASED FORMATION CONTROL PYTHON CODE 5 2: BEARING-BASED FORMATION CONTROL PYTHON CODE 5 3: ANGLE-BASED FORMATION CONTROL CONVEX OPTIMIZATION GROUP TESTING GRADIENT-BASED ALGORITHMS GRADIENT DESCENT ALGORITHM GRADIENT PROJECTION ALGORITHM SUBGRADIENT METHODS PROXIMAL ALGORITHMS PROXIMAL OPERATOR PROXIMAL GRADIENT ALGORITHM ADMM DISTRIBUTED SUBGRADIENT ALGORITHM DISTRIBUTED ADMM DISTRIBUTED ADMM WITH REGULARIZATION PYTHON CODE 6 1: GROUP TESTING BY CVXPY PYTHON CODE 6 2: GROUP TESTING BY GRADIENT PROJECTION PYTHON CODE 6 3: GROUP TESTING BY SUBGRADIENT METHOD PYTHON CODE 6 4: GROUP TESTING BY FISTA PYTHON CODE 6 5: GROUP TESTING BY DISTRIBUTED SUBGRADIENT PROJECTION PYTHON CODE 6 6: GROUP TESTING BY DISTRIBUTED ADMM PYTHON CODE 6 7: GROUP TESTING BY DISTRIBUTED ADMM WITH REGULARIZATION VIRAL SPREADING PHENOMENON VIRAL SPREADING PHENOMENON OVER COMPLEX NETWORKS MATHEMATICAL MODELS OF VIRAL SPREADING PHENOMENON SI MODEL SIS MODEL SIR MODEL SPREADING PHENOMENON OVER COMPLEX NETWORKS RANDOM NETWORKS VIRAL SPREADING OVER RANDOM NETWORKS MULTI-AGENT SIMULATION OF VIRAL SPREADING PYTHON CODE 7 1: SI MODEL PYTHON CODE 7 2: SIS MODEL PYTHON CODE 7 3: SIR MODEL PYTHON CODE 7 4: ERDÖS–RÉNYI RANDOM GRAPH PYTHON CODE 7 5: SCALE-FREE NETWORK PYTHON CODE 7 6: MULTI-AGENT SIMULATION OVER A COMPLEX NETWORK