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E-raamat: Mathematics Of Autonomy: Mathematical Methods For Cyber-physical-cognitive Systems

(Defence Science & Technology Group, Australia), (Defence Science & Technology Group, Australia), (Defence Science & Technology Group, Australia)
  • Formaat: 432 pages
  • Ilmumisaeg: 30-Oct-2017
  • Kirjastus: World Scientific Publishing Co Pte Ltd
  • Keel: eng
  • ISBN-13: 9789813230408
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Mathematics Of Autonomy: Mathematical Methods For Cyber-physical-cognitive SystemsSuurem pilt
  • Formaat: 432 pages
  • Ilmumisaeg: 30-Oct-2017
  • Kirjastus: World Scientific Publishing Co Pte Ltd
  • Keel: eng
  • ISBN-13: 9789813230408
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Three researchers at the Defence Science & Technology Group in Australia introduce the physics of cyber-physical-cognitive autonomy, and propose mathematical tools from quantum information and quantum computation adapted for modern theoretical autonomy. The graduate text explores perceptual control theory, extends the theoretical concept of 2D quantum turbulence to derive the analytical (closed-form) model of 3D turbulent wind flow, and presents recursive Bayesian techniques for cognitive estimation in autonomous systems and FastSLAM algorithms. Appendices give a thorough review of tensor methodology, classical neural networks, and artificial intelligence. Annotation ©2018 Ringgold, Inc., Portland, OR (protoview.com)

Mathematics of Autonomy provides solid mathematical foundations for building useful Autonomous Systems. It clarifies what makes a system autonomous rather than simply automated, and reveals the inherent limitations of systems currently incorrectly labeled as autonomous in reference to the specific and strong uncertainty that characterizes the environments they operate in. Such complex real-world environments demand truly autonomous solutions to provide the flexibility and robustness needed to operate well within them.This volume embraces hybrid solutions to demonstrate extending the classes of uncertainty autonomous systems can handle. In particular, it combines physical-autonomy (robots), cyber-autonomy (agents) and cognitive-autonomy (cyber and embodied cognition) to produce a rigorous subset of trusted autonomy: Cyber-Physical-Cognitive autonomy (CPC-autonomy).The body of the book alternates between underlying theory and applications of CPC-autonomy including "Autonomous Supervision of a Swarm of Robots" , "Using Wind Turbulence against a Swarm of UAVs" and "Unique Super-Dynamics for All Kinds of Robots (UAVs, UGVs, UUVs and USVs)" to illustrate how to effectively construct Autonomous Systems using this model. It avoids the wishful thinking that characterizes much discussion related to autonomy, discussing the hard limits and challenges of real autonomous systems. In so doing, it clarifies where more work is needed, and also provides a rigorous set of tools to tackle some of the problem space.
Preface v
Acknowledgments vii
Glossary of Acronyms ix
Glossary of Symbols xiii
1 Introduction
1(46)
1.1 Autonomous Systems
1(5)
1.1.1 What is an Autonomous System?
2(4)
1.2 What is Trust and Why Do We Need It?
6(8)
1.2.1 Inter Human Trust H trusts H
7(2)
1.2.2 Inter Machine Trust A trusts A
9(2)
1.2.3 Human Trust of Machines H trusts A
11(2)
1.2.4 Machines Trusting Humans A trusts H
13(1)
1.3 Motivations from Uncertainty
14(5)
1.4 Cyber-Physical-Cognitive (CPC) Autonomy: A Rigorous Model of Trusted Autonomy
19(1)
1.5 Technical Preliminaries
20(27)
1.5.1 Linear Control Preliminaries
20(3)
1.5.2 Pictorial Reasoning
23(4)
1.5.3 Tensors
27(9)
1.5.4 Mechanics of Autonomous Vehicles
36(1)
1.5.5 Quantum Entanglement: ER = EPR
37(5)
1.5.6 Second-Quantization Formalism
42(5)
2 Physics of the CPC-Autonomy: Port-Hamiltonian Dynamics and Control of Multi-Physical Networks
47(22)
2.1 Introduction to Port-Hamiltonian Modeling of Multi-Physical Networks
47(13)
2.1.1 PHS Background
47(4)
2.1.2 Informal PHS Description
51(1)
2.1.3 Gradient Operator and Gradient Descent
51(1)
2.1.4 PHS Definition
51(1)
2.1.5 First PHS Example: An LCL-Circuit
52(1)
2.1.6 Poisson Structure
53(1)
2.1.7 Open Port-Hamiltonian Systems
54(1)
2.1.8 Interconnection of Port-Hamiltonian Systems
54(1)
2.1.9 Including Dissipation
54(1)
2.1.10 Dirac Structure
55(1)
2.1.11 Composition of Dirac Structures
56(1)
2.1.12 Control by Interconnection
56(1)
2.1.13 Passive Control Systems
57(2)
2.1.14 Second PHS Example: Mass-Spring-Damper System
59(1)
2.2 Dirac Structures on Directed Graphs
60(3)
2.2.1 Dirac Structures
60(1)
2.2.2 Directed Graphs or Digraphs
61(1)
2.2.3 Dirac Structures on Digraphs
61(1)
2.2.4 PHS with Dirac Structures on Digraphs
62(1)
2.3 Category-Theoretic Abstraction: Deductive Reasoning on Graphs
63(6)
2.3.1 Digraphs as Deductive Systems
63(1)
2.3.2 Cartesian Closed Deductive Systems and Categories
64(1)
2.3.3 Basics of Topos Theory and Intuitionistic Logic
64(5)
3 CPC-Application: Autonomous Brain-Like Supervisor for a Swarm of Robots
69(12)
3.1 Hamiltonian Control for a Robotic Swarm
70(1)
3.2 Nobel-Awarded Hippocampal Navigation System
71(2)
3.3 Adaptive Path Integral Model for the Hippocampal Navigation System
73(3)
3.4 Coupled Nonlinear Schrodinger Equations
76(5)
3.4.1 Special Case: Analytical Soliton
76(1)
3.4.2 General Case: Numerical Simulation
77(4)
4 Micro-Cognitive CPC-Autonomy: Quantum Computational Tensor Networks
81(24)
4.1 CPC-Autonomy in the Language of Quantum Information and Computation
81(1)
4.2 Entropy, the First Law of Entanglement and the Holographic Principle
82(2)
4.3 A Field-Theoretic Background
84(1)
4.4 Tensor Product of Hilbert Spaces and the Logic of Entanglement
85(1)
4.5 Introduction to Tensor Networks
86(1)
4.6 Formal Definition of Tensor Networks
87(4)
4.6.1 Contraction of Tensor Networks
87(1)
4.6.2 Wave Function of Quantum Many-Body States
88(1)
4.6.3 Matrix Product States TNs
89(2)
4.7 Simple TN-Simulation in TNTgo!
91(1)
4.8 Fermionic Tensor Networks
91(5)
4.9 CPC-Application: Entangled Quantum Computation for Swarm Intelligence
96(9)
4.9.1 Quantum-Computational Fusion
98(3)
4.9.2 Entangled Swarm Intelligence Model
101(4)
5 Cyber-Cognitive CPC-Autonomy: TensorFlow and Deep Neural Tensor Networks
105(22)
5.1 Modern Brain Models: Deep Learning Neural Networks
105(8)
5.1.1 Introduction to Deep Learning
105(2)
5.1.2 Deep Belief Networks (DBNs) using Restricted Boltzmann Machines (RBMs)
107(3)
5.1.3 Recurrent Neural Nets (RNNs)
110(1)
5.1.4 Convolutional Neural Networks (ConvNets)
111(2)
5.2 TensorFlow: The State-of-the-Art in Machine Learning
113(4)
5.3 Tensor Decompositions for Deep Representation Learning
117(3)
5.3.1 Multi-Task Representation Learning: Shallow and Deep
117(1)
5.3.2 Basics of Tensor Factorization
118(1)
5.3.3 Knowledge Sharing Between the Tasks
118(1)
5.3.4 Tensor Decompositions
119(1)
5.3.5 Deep Multi-Task Representation Learning
119(1)
5.4 Generalized Tensor Decompositions in ConvNets
120(7)
5.4.1 Introducing ConvNets
120(1)
5.4.2 Tensors in ConvNets
120(1)
5.4.3 Generalized Tensor Decompositions
121(1)
5.4.4 A Typical ConvNet Architecture
121(1)
5.4.5 ConvNet Classification
122(1)
5.4.6 Grid Tensors for Shallow and Deep ConvNets
123(1)
5.4.7 From Tensors to Matrices in ConvNets
124(3)
6 Cognitive Control in CPC-Autonomy: Perceptual Control Theory and Its Alternatives
127(54)
6.1 Brief Introduction to Perceptual Control Theory (PCT)
127(2)
6.2 Predecessors of PCT: Wiener's Cybernetics, Beinstein's Neural Control and Gardner's Cognitive Control
129(10)
6.2.1 Wiener's Cybernetics and Linear Control Theory
129(1)
6.2.2 Primary Control Example: Inverted Pendulum Balance
129(7)
6.2.3 Bernstein's Neural Control and Motion Pattern Architecture
136(2)
6.2.4 Gardner's Cognitive Control: Cognitive Behavior and Adaptation
138(1)
6.3 PCT Fundamentals
139(6)
6.3.1 Controlled Variables in Psychology
139(2)
6.3.2 Marken's PCT Tracking Tests
141(4)
6.4 PCT Approach to Inverted Pendulum Balance
145(1)
6.5 PCT in Psychotherapy: Method of Levels
146(1)
6.6 PCT versus Brooks' Subsumption Architecture
147(2)
6.7 PCT Alternative 1: Lewinian Psycho--Physical Group Dynamics
149(3)
6.8 PCT Alternative 2: Model Predictive Control
152(5)
6.8.1 MPC Application: Control of a Rotational Spacecraft Model
154(1)
6.8.2 MPC-Based Mean-Field Games for Multi-Agent CPC-Autonomy
155(2)
6.9 PCT Alternative 3: Synergetics Approach to CPC-Autonomy
157(5)
6.9.1 Nonequilibrium Phase Transitions
160(2)
6.10 A Model-Free PCT Alternative: Adaptive Fuzzy Inference for Human-Like Decision and Control
162(19)
6.10.1 Motivation: Why Adaptive Fuzzy Inference?
162(2)
6.10.2 Standard Fuzzy Control Example: Balancing an Inverted Pendulum
164(2)
6.10.3 History and Basics of Fuzzy Logic
166(1)
6.10.4 Fuzzy Inference System
167(2)
6.10.5 Fuzzy Control Basics
169(1)
6.10.6 Two Detailed Fuzzy Control Examples
170(3)
6.10.7 Conclusion: When to Use Adaptive Fuzzy Inference?
173(1)
6.10.8 Mathematical Takagi-Sugeno Fuzzy Dynamics
174(7)
7 CPC-Application: Using Wind Turbulence against a Team of UAVs
181(16)
7.1 Analytical Model of Turbulent Wind Flow
181(5)
7.1.1 Closed-Form Solutions of the NLSE
183(1)
7.1.2 A 10-Component Wind Turbulence Soliton Model
184(2)
7.1.3 3D Turbulent Wind Flow Model
186(1)
7.2 UAVs Sophisticated 3D Collision Avoidance System
186(6)
7.3 Simulating Soft Attrition of a Team of UAVs using the 3D Wind Flow Model
192(5)
8 Cognitive Estimation in CPC-Autonomy: Recursive Bayesian Filters and FastSLAM Algorithms
197(38)
8.1 Bayesian Probability Basics
197(1)
8.2 Kalman's State-Space LQR/LQG Control Systems
198(3)
8.2.1 State-Space Formulation for Linear MIMO Systems
198(1)
8.2.2 Linear Stationary Systems and Operators
199(1)
8.2.3 Kalman's LQR/LQG Controller
199(2)
8.3 Kalman Filtering Basics
201(12)
8.3.1 Classical (Linear) Kalman Filter
202(7)
8.3.2 Extended (Nonlinear) Kalman Filter
209(1)
8.3.3 Unscented Kalman Filter
210(2)
8.3.4 Ensemble Kalman Filter and Nonlinear Estimation
212(1)
8.4 General Bayesian Filter and Cognitive Control
213(10)
8.4.1 Bayesian Filter
214(2)
8.4.2 Cognitive Dynamic and Control
216(2)
8.4.3 Bayesian Programming Framework with Robotic Applications
218(5)
8.5 Particle Filters: Superior Estimation Models for CPC-Autonomy
223(4)
8.5.1 Particle Filtering Basics
225(2)
8.6 Low-Dimensional FastSLAM Algorithms
227(2)
8.7 High-Dimensional FastSLAM Algorithms
229(6)
9 CPC Super-Dynamics for a Universal Large-Scale Autonomous Operation
235(20)
9.1 Introduction
235(3)
9.2 Lagrangian and Hamiltonian Fleets/Swarms
238(6)
9.2.1 Basic Newton-Euler Mechanics of Individual Unmanned Vehicles
238(2)
9.2.2 Lagrangian Dynamics and Control for a Water (USV + UUV) Fleet
240(3)
9.2.3 Hamiltonian Dynamics and Control for an Air (UGV + UAV) Swarm
243(1)
9.3 Super-Dynamics for the Universal (UGV + UAV + USV + UUV) Fleet
244(5)
9.3.1 Super-Dynamics Formalism on a Kahler 4n-Manifold
244(4)
9.3.2 Super-Dynamics Application: 3D Simulation in an Urban Environment
248(1)
9.4 Continuous Super-Dynamics for a Very Large Fleet
249(6)
10 Appendix 1: The World of Tensors
255(48)
10.1 Abstract Tensor Algebra and Geometry
255(1)
10.2 Tensors on Smooth Manifolds
256(6)
10.2.1 Vector-Fields and Commutators on Configuration Manifolds
256(1)
10.2.2 Metric Tensor
257(1)
10.2.3 Tensor Derivative V-Operator (Connection)
258(2)
10.2.4 Riemann and Ricci Curvature Tensors
260(1)
10.2.5 Geodesies and Geodesic Deviation
261(1)
10.3 Basic Lie Groups and Lie Derivatives
262(4)
10.3.1 Lie Groups and Their Lie Algebras
262(3)
10.3.2 Lie Derivative and Killing Vector-Fields
265(1)
10.4 Basic Applications to General Nonlinear Dynamics
266(4)
10.4.1 The Phase-Space Formalism of (Co)tangent Bundles
266(2)
10.4.2 A Generic Tensor Model for a `Social-Game Situation'
268(2)
10.5 Exterior Differential Forms
270(9)
10.5.1 The Closure Principle: `Boundary of a Boundary is Zero'
271(2)
10.5.2 Hodge's and Maxwell's Theories
273(5)
10.5.3 Cartan Calculus
278(1)
10.5.4 Gauge Potential, Field Strength and Cartan's Equations
278(1)
10.6 Basic Physical Applications: From Einstein to Quantum
279(12)
10.6.1 Special Relativity
280(2)
10.6.2 General Relativity
282(1)
10.6.3 Homogeneous Cosmological Models
283(1)
10.6.4 Canonical Quantization
284(1)
10.6.5 Hodge Decomposition and Gauge Path Integral
285(6)
10.7 Computational Tensor Framework in Mathematica®
291(12)
10.7.1 Computing with Abstract and Riemannian Tensors
291(6)
10.7.2 Computing with Exterior Differential Forms
297(6)
11 Appendix 2: Classical Neural Networks and AI
303(50)
11.1 Classical Artificial Neural Networks as Simplistic Brain Models
303(42)
11.1.1 Biological Versus Artificial Neural Nets (ANNs)
304(1)
11.1.2 Most Popular Classical Discrete ANNs
305(16)
11.1.3 Most Popular Classical Continuous ANNs
321(5)
11.1.4 Recurrent Neural Nets (RNNs)
326(4)
11.1.5 Grossberg's Adaptive Resonance Theory
330(2)
11.1.6 Hopfield's Associative RNNs
332(7)
11.1.7 Kosko's Bidirectional Competitive RNNs
339(2)
11.1.8 Support Vector Machines (SVMs)
341(3)
11.1.9 Spiking Neural Nets as Axonal Brain Models
344(1)
11.2 Current Research in AI and Supercomputing
345(8)
11.2.1 Strong AI vs. Weak AI
348(1)
11.2.2 IBM's Watson and TrueNorth vs. Top Supercomputers
349(4)
Bibliography 353(42)
Index 395
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