Mathematics of autonomy: mathematical methods for cyber-physical-cognitive systems
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New Jersey
World Scientific
2018
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references (pages 353-394) and index |
| Beschreibung: | xxii, 409 Seiten Illustrationen 24 cm |
| ISBN: | 9789813230385 |
Internformat
MARC
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| 100 | 1 | |a Ivancevic, Vladimir G. |4 aut | |
| 245 | 1 | 0 | |a Mathematics of autonomy |b mathematical methods for cyber-physical-cognitive systems |c Vladimir G. Ivancevic (Defence Science & Technology Group, Australia), Darryn J. Reid (Defence Science & Technology Group, Australia), Michael J. Pilling Defence Science & Technology Group, Australia |
| 264 | 1 | |a New Jersey |b World Scientific |c 2018 | |
| 300 | |a xxii, 409 Seiten |b Illustrationen |c 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Includes bibliographical references (pages 353-394) and index | ||
| 650 | 4 | |a Intelligent control systems |x Mathematics | |
| 650 | 4 | |a Self-organizing systems |x Mathematical models | |
| 650 | 4 | |a Cooperating objects (Computer systems) | |
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| 700 | 1 | |a Reid, Darryn J. |4 aut | |
| 700 | 1 | |a Pilling, M. J. |4 aut | |
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Datensatz im Suchindex
| _version_ | 1804178696915910656 |
|---|---|
| adam_text | Contents
Preface............................................................ v
Acknowledgments.................................................. vii
Glossary of Acronyms.............................................. ix
Glossary of Symbols............................................. xiii
1 Introduction................................................... 1
1.1 Autonomous Systems........................................ 1
1.1.1 What is an Autonomous System?....................... 2
1.2 What is Trust and Why Do We Need It?..................... 6
1.2.1 Inter Human Trust HI trusts HI...................... 7
1.2.2 Inter Machine Trust A trusts A...................... 9
1.2.3 Human Trust of Machines HI trusts A................ 11
1.2.4 Machines Trusting Humans A trusts HI .............. 13
1.3 Motivations from Uncertainty............................. 14
1.4 Cyber-Physical-Cognitive (CPC) Autonomy: A Rigorous
Model of Trusted Autonomy................................ 19
1.5 Technical Preliminaries.................................. 20
1.5.1 Linear Control Preliminaries....................... 20
1.5.2 Pictorial Reasoning................................ 23
1.5.3 Tensors............................................ 27
1.5.4 Mechanics of Autonomous Vehicles................... 36
1.5.5 Quantum Entanglement: ER = EPR..................... 37
1.5.6 Second-Quantization Formalism...................... 42
2 Physics of the CPC-Autonomy: Port-Hamiltonian
Dynamics and Control of Multi-Physical Networks .............. 47
2.1 Introduction to Port-Hamiltonian Modeling of Multi-Physical
Networks................................................. 47
2.1.1 PHS Background..................................... 47
xviii Contents
2.1.2 Informal PHS Description............................ 51
2.1.3 Gradient Operator and Gradient Descent.............. 51
2.1.4 PHS Definition...................................... 51
2.1.5 First PHS Example: An LCL-Circuit................... 52
2.1.6 Poisson Structure .................................. 53
2.1.7 Open Port-Hamiltonian Systems ...................... 54
2.1.8 Interconnection of Port-Hamiltonian Systems......... 54
2.1.9 Including Dissipation............................... 54
2.1.10 Dirac Structure.................................... 55
2.1.11 Composition of Dirac Structures ................... 56
2.1.12 Control by Interconnection......................... 56
2.1.13 Passive Control Systems............................ 57
2.1.14 Second PHS Example: Mass-Spring-Damper System ... 59
2.2 Dirac Structures on Directed Graphs....................... 60
2.2.1 Dirac Structures ................................... 60
2.2.2 Directed Graphs or Digraphs ........................ 61
2.2.3 Dirac Structures on Digraphs........................ 61
2.2.4 PHS with Dirac Structures on Digraphs............... 62
2.3 Category-Theoretic Abstraction: Deductive Reasoning on
Graphs.................................................... 63
2.3.1 Digraphs as Deductive Systems ...................... 63
2.3.2 Cartesian Closed Deductive Systems and Categories ... 64
2.3.3 Basics of Topos Theory and Intuitionistic Logic..... 64
3 CPC-Application: Autonomous Brain-Like Supervisor for
a Swarm of Robots.............................................. 69
3.1 Hamiltonian Control for a Robotic Swarm................... 70
3.2 Nobel-Awarded Hippocampal Navigation System............... 71
3.3 Adaptive Path Integral Model for the Hippocampal
Navigation System......................................... 73
3.4 Coupled Nonlinear Schrodinger Equations................... 76
3.4.1 Special Case: Analytical Soliton.................... 76
3.4.2 General Case: Numerical Simulation.................. 77
4 Micro-Cognitive CPC-Autonomy: Quantum
Computational Tensor Networks.................................. 81
4.1 CPC-Autonomy in the Language of Quantum Information
and Computation........................................... 81
4.2 Entropy, the First Law of Entanglement and the Holographic
Principle................................................. 82
4.3 A Field-Theoretic Background.............................. 84
4.4 Tensor Product of Hilbert Spaces and the Logic of
Entanglement.............................................. 85
4.5 Introduction to Tensor Networks........................... 86
4.6 Formal Definition of Tensor Networks...................... 87
Contents
xix
4.6.1 Contraction of Tensor Networks...................... 87
4.6.2 Wave Function of Quantum Many-Body States........... 88
4.6.3 Matrix Product States TNs........................... 89
4.7 Simple TN-Simulation in TNTgo! ........................... 91
4.8 Fermionic Tensor Networks................................. 91
4.9 CPC-Application: Entangled Quantum Computation for
Swarm Intelligence ....................................... 96
4.9.1 Quantum-Computational Fusion ....................... 98
4.9.2 Entangled Swarm Intelligence Model..................101
5 Cyber-Cognitive CPC-Autonomy: TensorFlow and Deep
Neural Tensor Networks.........................................105
5.1 Modern Brain Models: Deep Learning Neural Networks .......105
5.1.1 Introduction to Deep Learning.......................105
5.1.2 Deep Belief Networks (DBNs) using Restricted
Boltzmann Machines (RBMs)...........................107
5.1.3 Recurrent Neural Nets (RNNs)........................110
5.1.4 Convolutional Neural Networks (ConvNets)............Ill
5.2 TensorFlow: The State-of-the-Art in Machine Learning......113
5.3 Tensor Decompositions for Deep Representation Learning .... 117
5.3.1 Multi-Task Representation Learning: Shallow and Deep 117
5.3.2 Basics of Tensor Factorization......................118
5.3.3 Knowledge Sharing Between the Tasks.................118
5.3.4 Tensor Decompositions...............................119
5.3.5 Deep Multi-Task Representation Learning.............119
5.4 Generalized Tensor Decompositions in ConvNets.............120
5.4.1 Introducing ConvNets................................120
5.4.2 Tensors in ConvNets.................................120
5.4.3 Generalized Tensor Decompositions...................121
5.4.4 A Typical ConvNet Architecture......................121
5.4.5 ConvNet Classification..............................122
5.4.6 Grid Tensors for Shallow and Deep ConvNets..........123
5.4.7 From Tensors to Matrices in ConvNets................124
6 Cognitive Control in CPC-Autonomy: Perceptual Control
Theory and Its Alternatives ...................................127
6.1 Brief Introduction to Perceptual Control Theory (PCT).....127
6.2 Predecessors of PCT: Wiener’s Cybernetics, Beinstein’s
Neural Control and Gardner’s Cognitive Control ...........129
6.2.1 Wiener’s Cybernetics and Linear Control Theory......129
6.2.2 Primary Control Example: Inverted Pendulum Balance. 129
6.2.3 Bernstein’s Neural Control and Motion Pattern
Architecture........................................136
6.2.4 Gardner’s Cognitive Control: Cognitive Behavior and
Adaptation..........................................138
XX
Contents
6.3 PCT Fundamentals..........................................139
6.3.1 Controlled Variables in Psychology..................139
6.3.2 Marken’s PCT Tracking Tests........................141
6.4 PCT Approach to Inverted Pendulum Balance.................145
6.5 PCT in Psychotherapy: Method of Levels....................146
6.6 PCT versus Brooks’ Subsumption Architecture...............147
6.7 PCT Alternative 1: Lewinian Psycho- Physical Group
Dynamics ................................................149
6.8 PCT Alternative 2: Model Predictive Control...............152
6.8.1 MPC Application: Control of a Rotational Spacecraft
Model .............................................154
6.8.2 MPC-Based Mean-Field Games for Multi-Agent
CPC-Autonomy.......................................155
6.9 PCT Alternative 3: Synergetics Approach to CPC-Autonomy . 157
6.9.1 Nonequilibrium Phase Transitions...................160
6.10 A Model-Free PCT Alternative: Adaptive Fuzzy Inference for
Human-Like Decision and Control..........................162
6.10.1 Motivation: Why Adaptive Fuzzy Inference?.........162
6.10.2 Standard Fuzzy Control Example: Balancing an
Inverted Pendulum..................................164
6.10.3 History and Basics of Fuzzy Logic.................166
6.10.4 Fuzzy Inference System............................167
6.10.5 Fuzzy Control Basics .............................169
6.10.6 Two Detailed Fuzzy Control Examples...............170
6.10.7 Conclusion: When to Use Adaptive Fuzzy Inference? .. . 173
6.10.8 Mathematical Takagi—Sugeno Fuzzy Dynamics.........174
7 CPC-Application: Using Wind Turbulence against a
Team of UAVs..................................................181
7.1 Analytical Model of Turbulent Wind Flow..................181
7.1.1 Closed-Form Solutions of the NLSE..................183
7.1.2 A 10-Component Wind Turbulence Soliton Model.184
7.1.3 3D Turbulent Wind Flow Model.......................186
7.2 UAV’s Sophisticated 3D Collision Avoidance System........186
7.3 Simulating Soft Attrition of a Team of UAVs using the 3D
Wind Flow Model..........................................192
8 Cognitive Estimation in CPC-Autonomy: Recursive
Bayesian Filters and FastSLAM Algorithms .....................197
8.1 Bayesian Probability Basics..............................197
8.2 Kalman’s State-Space LQR/LQG Control Systems.............198
8.2.1 State-Space Formulation for Linear MIMO Systems .... 198
8.2.2 Linear Stationary Systems and Operators ...199
8.2.3 Kalman’s LQR/LQG Controller........................199
8.3 Kalman Filtering Basics..................................201
Contents
xxi
8.3.1 Classical (Linear) Kalman Filter ..................202
8.3.2 Extended (Nonlinear) Kalman Filter.................209
8.3.3 Unscented Kalman Filter............................210
8.3.4 Ensemble Kalman Filter and Nonlinear Estimation .... 212
8.4 General Bayesian Filter and Cognitive Control............213
8.4.1 Bayesian Filter....................................214
8.4.2 Cognitive Dynamic and Control......................216
8.4.3 Bayesian Programming Framework with Robotic
Applications.......................................218
8.5 Particle Filters: Superior Estimation Models for
CPC-Autonomy.............................................223
8.5.1 Particle Filtering Basics..........................225
8.6 Low-Dimensional FastSLAM Algorithms .....................227
8.7 High-Dimensional FastSLAM Algorithms.....................229
9 CPC Super-Dynamics for a Universal Large-Scale
Autonomous Operation..........................................235
9.1 Introduction.............................................235
9.2 Lagrangian and Hamiltonian Fleets/Swarms.................238
9.2.1 Basic Newton-Euler Mechanics of Individual
Unmanned Vehicles..................................238
9.2.2 Lagrangian Dynamics and Control for a Water (USV
+ UUV) Fleet ......................................240
9.2.3 Hamiltonian Dynamics and Control for an Air (UGV
+ UAV) Swarm.......................................243
9.3 Super-Dynamics for the Universal (UGV + UAV + USV +
UUV) Fleet...............................................244
9.3.1 Super-Dynamics Formalism on a Kahler 4n-Manifold . . 244
9.3.2 Super-Dynamics Application: 3D Simulation in an
Urban Environment .................................248
9.4 Continuous Super-Dynamics for a Very Large Fleet.........249
10 Appendix 1: The World of Tensors ............................255
10.1 Abstract Tensor Algebra and Geometry....................255
10.2 Tensors on Smooth Manifolds.............................256
10.2.1 Vector-Fields and Commutators on Configuration
Manifolds..........................................256
10.2.2 Metric Tensor.....................................257
10.2.3 Tensor Derivative V-Operator (Connection) ........258
10.2.4 Riemann and Ricci Curvature Tensors...............260
10.2.5 Geodesics and Geodesic Deviation..................261
10.3 Basic Lie Groups and Lie Derivatives....................262
10.3.1 Lie Groups and Their Lie Algebras.................262
10.3.2 Lie Derivative and Killing Vector-Fields..........265
10.4 Basic Applications to General Nonlinear Dynamics........266
xxii Contents
10.4.1 The Phase-Space Formalism of (Co)tangent Bundles .. . 266
10.4.2 A Generic Tensor Model for a ‘Social-Game Situation’ . 268
10.5 Exterior Differential Forms.................................270
10.5.1 The Closure Principle: ‘Boundary of a Boundary is
Zero’ .................................................271
10.5.2 Hodge’s and Maxwell’s Theories........................273
10.5.3 Cartan Calculus.......................................278
10.5.4 Gauge Potential, Field Strength and Cartan’s
Equations..............................................278
10.6 Basic Physical Applications: From Einstein to Quantum.......279
10.6.1 Special Relativity....................................280
10.6.2 General Relativity....................................282
10.6.3 Homogeneous Cosmological Models.......................283
10.6.4 Canonical Quantization................................284
10.6.5 Hodge Decomposition and Gauge Path Integral......285
10.7 Computational Tensor Framework in Mathematical .............291
10.7.1 Computing with Abstract and Riemannian Tensors .... 291
10.7.2 Computing with Exterior Differential Forms...........297
11 Appendix 2: Classical Neural Networks and AI......................303
11.1 Classical Artificial Neural Networks as Simplistic Brain
Models.......................................................303
11.1.1 Biological Versus Artificial Neural Nets (ANNs).......304
11.1.2 Most Popular Classical Discrete ANNs..................305
11.1.3 Most Popular Classical Continuous ANNs................321
11.1.4 Recurrent Neural Nets (RNNs)..........................326
11.1.5 Grossberg’s Adaptive Resonance Theory ................330
11.1.6 Hopfield’s Associative RNNs...........................332
11.1.7 Kosko’s Bidirectional Competitive RNNs................339
11.1.8 Support Vector Machines (SVMs) .......................341
11.1.9 Spiking Neural Nets as Axonal Brain Models ...........344
11.2 Current Research in AI and Supercomputing....................345
11.2.1 Strong AI vs. Weak AI.................................348
11.2.2 IBM’s Watson and TrueNorth vs. Top Supercomputers . 349
Bibliography...........................................................353
Index..................................................................395
|
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| illustrated | Illustrated |
| indexdate | 2024-07-10T08:08:05Z |
| institution | BVB |
| isbn | 9789813230385 |
| language | English |
| lccn | 017039522 |
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| physical | xxii, 409 Seiten Illustrationen 24 cm |
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| spelling | Ivancevic, Vladimir G. aut Mathematics of autonomy mathematical methods for cyber-physical-cognitive systems Vladimir G. Ivancevic (Defence Science & Technology Group, Australia), Darryn J. Reid (Defence Science & Technology Group, Australia), Michael J. Pilling Defence Science & Technology Group, Australia New Jersey World Scientific 2018 xxii, 409 Seiten Illustrationen 24 cm txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references (pages 353-394) and index Intelligent control systems Mathematics Self-organizing systems Mathematical models Cooperating objects (Computer systems) Kontrolltheorie (DE-588)4032317-1 gnd rswk-swf Selbst organisierendes System (DE-588)4054424-2 gnd rswk-swf Kontrolltheorie (DE-588)4032317-1 s Selbst organisierendes System (DE-588)4054424-2 s DE-604 Reid, Darryn J. aut Pilling, M. J. aut Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030472329&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ivancevic, Vladimir G. Reid, Darryn J. Pilling, M. J. Mathematics of autonomy mathematical methods for cyber-physical-cognitive systems Intelligent control systems Mathematics Self-organizing systems Mathematical models Cooperating objects (Computer systems) Kontrolltheorie (DE-588)4032317-1 gnd Selbst organisierendes System (DE-588)4054424-2 gnd |
| subject_GND | (DE-588)4032317-1 (DE-588)4054424-2 |
| title | Mathematics of autonomy mathematical methods for cyber-physical-cognitive systems |
| title_auth | Mathematics of autonomy mathematical methods for cyber-physical-cognitive systems |
| title_exact_search | Mathematics of autonomy mathematical methods for cyber-physical-cognitive systems |
| title_full | Mathematics of autonomy mathematical methods for cyber-physical-cognitive systems Vladimir G. Ivancevic (Defence Science & Technology Group, Australia), Darryn J. Reid (Defence Science & Technology Group, Australia), Michael J. Pilling Defence Science & Technology Group, Australia |
| title_fullStr | Mathematics of autonomy mathematical methods for cyber-physical-cognitive systems Vladimir G. Ivancevic (Defence Science & Technology Group, Australia), Darryn J. Reid (Defence Science & Technology Group, Australia), Michael J. Pilling Defence Science & Technology Group, Australia |
| title_full_unstemmed | Mathematics of autonomy mathematical methods for cyber-physical-cognitive systems Vladimir G. Ivancevic (Defence Science & Technology Group, Australia), Darryn J. Reid (Defence Science & Technology Group, Australia), Michael J. Pilling Defence Science & Technology Group, Australia |
| title_short | Mathematics of autonomy |
| title_sort | mathematics of autonomy mathematical methods for cyber physical cognitive systems |
| title_sub | mathematical methods for cyber-physical-cognitive systems |
| topic | Intelligent control systems Mathematics Self-organizing systems Mathematical models Cooperating objects (Computer systems) Kontrolltheorie (DE-588)4032317-1 gnd Selbst organisierendes System (DE-588)4054424-2 gnd |
| topic_facet | Intelligent control systems Mathematics Self-organizing systems Mathematical models Cooperating objects (Computer systems) Kontrolltheorie Selbst organisierendes System |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030472329&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT ivancevicvladimirg mathematicsofautonomymathematicalmethodsforcyberphysicalcognitivesystems AT reiddarrynj mathematicsofautonomymathematicalmethodsforcyberphysicalcognitivesystems AT pillingmj mathematicsofautonomymathematicalmethodsforcyberphysicalcognitivesystems |