New trends in control theory

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Title:

Personal Author:

Ivancevic, Vladimir G.

Series:

Series on stability, vibration and control of systems. Series A ; v. 19.

Series on stability, vibration, and control of systems. Series A ; v. 19.

Publication Information:

Singapore ; World Scientific, 2013.

Physical Description:

xiii, 722 p. : ill. ; 24 cm.

ISBN:

9789814425940

Subject Term:

Control theory.

Added Author:

Ivancevic, Tijana T.

Available:*

Library	Item Barcode	Call Number	Material Type	Item Category 1	Status
Searching... PSZ KL	30000010239533	QA402.3 I93 2013	Open Access Book	Book	Searching... Unknown

New Trends in Control Theory is a graduate-level monographic textbook. It is a contemporary overview of modern trends in control theory. The introductory chapter gives the geometrical and quantum background, which is a necessary minimum for comprehensive reading of the book. The second chapter gives the basics of classical control theory, both linear and nonlinear. The third chapter shows the key role that Euclidean group of rigid motions plays in modern robotics and biomechanics. The fourth chapter gives an overview of modern quantum control, from both theoretical and measurement perspectives. The fifth chapter presents modern control and synchronization methods in complex systems and human crowds. The appendix provides the rest of the background material complementary to the introductory chapter.The book is designed as a one-semester course for engineers, applied mathematicians, computer scientists and physicists, both in industry and academia. It includes a most relevant bibliography on the subject and detailed index.

1 Introduction	p. 1
1.1 Geometrical Preliminaries	p. 1
1.1.1 Variational Method of Classical Mechanics	p. 1
1.1.2 Lie Algebra Mechanics	p. 4
1.1.3 Covariant Dynamics Modelling	p. 10
1.1.4 Exterior Differential Forms	p. 14
1.1.5 Hodge Theory Basics	p. 19
1.1.6 Principal G-Bundles, Connections and G-Snakes	p. 25
1.1.7 Wei-Norman Exponential Method	p. 29
1.2 Quantum Preliminaries	p. 34
1.2.1 Basic Quantum Mechanics	p. 34
1.2.2 Basic Quantum Fields	p. 48
1.2.3 Wigner Function Basics	p. 58
1.2.4 Path Integral Quantization	p. 60
1.2.5 Gauge Path-Integral via Hodge Decomposition	p. 65
2 Basics of Classical Control Theory	p. 69
2.1 Linear Systems and Signals	p. 69
2.1.1 Laplace Transform and Transfer-Function Methods	p. 69
2.1.2 Fourier and Wavelet Transforms for Linear Signals	p. 74
2.1.3 Kalman's Modular State-Space and Filtering Methods	p. 93
2.1.4 Controllability of Linear Systems	p. 106
2.1.5 Stability of Linear Systems	p. 110
2.1.6 Naive Approaches to Nonlinear Systems	p. 113
2.2 Nonlinear Control Systems	p. 129
2.2.1 Command/Control in Human-Robot Interactions	p. 129
2.2.2 Nonlinear Controllability	p. 133
2.2.3 Basics of Geometric Nonlinear Control	p. 134
2.2.4 Lie-Derivative Based Nonlinear Feedback Control	p. 148
2.2.5 Hamiltonian Optimal Control and Maximum Principle	p. 150
2.2.6 Path-Integral Optimal Control of Stochastic Systems	p. 155
2.2.7 Fuzzy-Logic Control	p. 159
3 Euclidean Group in Modern Robotics and Biomechanics	p. 179
3.1 Introduction to Euclidean Group	p. 179
3.1.1 Euclidean Kinematics	p. 181
3.1.2 Basic Dynamics on SE(3)	p. 184
3.1.3 Coupled Newton-Euler Dynamics on SE(3)	p. 186
3.1.4 Introduction to Hamiltonian Biomechanics	p. 189
3.1.5 Library of Basic Hamiltonian Systems	p. 195
3.2 Euclidean Group in Modern Robotics	p. 202
3.2.1 Constructive Controllability for Motion on Lie Groups	p. 202
3.2.2 SE(3)-Group Control Example	p. 203
3.2.3 Examples of SE(3)-Subgroups Control	p. 207
3.2.4 Nonholonomic Dynamics of a Snakeboard	p. 210
3.2.5 Nonholonomic Kinematics of Snakes on Lie Groups	p. 212
3.2.6 Left-Invariant Kinematic Control Systems	p. 216
3.2.7 Geometrical Integration and Optimal Control on SE(3)	p. 222
3.2.8 Euclidean-Invariant Lagrangians	p. 226
3.2.9 Dynamical Games on SE(2)	p. 233
3.2.10 Nonholonomic Robotics and Their Optimal Control	p. 240
3.3 Euclidean Group in Modern Biomechanics	p. 246
3.3.1 Humanoid Robotics vs. Human Biodynamics	p. 250
3.3.2 Euclidean Jolt in Modern Injury Mechanics	p. 278
4 Quantum Control: Theory and Measurement	p. 293
4.1 Introduction to Quantum Control	p. 293
4.1.1 Real-Time Quantum Feedback Control	p. 296
4.1.2 Kraus Maps and Superoperator Formalism	p. 297
4.1.3 Symplectic Propagators and Rotating Waves	p. 304
4.2 Quantum Stochastic Systems: H ∞ and LQG Controls	p. 306
4.2.1 Linear Quantum Stochastic Systems	p. 306
4.2.2 Physical Realizability of Linear QSDEs	p. 308
4.2.3 Dissipation Properties	p. 310
4.2.4 H ∞ Controller Synthesis	p. 313
4.2.5 Quantum LQG Problem Formulation	p. 316
4.2.6 From LQG to LMI Problem	p. 319
4.2.7 LQG Controller Design Example	p. 324
4.3 Quantum Control Landscapes	p. 325
4.3.1 Introducing Quantum Control Landscapes	p. 325
4.3.2 Typical Quantum Control Problems	p. 328
4.3.3 Gradient and Hessian formulas	p. 329
4.3.4 The Control Objective	p. 333
4.3.5 Control of Quantum Gates	p. 337
4.3.6 Geometry of Quantum Control Landscapes	p. 339
4.3.7 State and Gate Control Problems and Solutions	p. 345
4.3.8 Level Sets of Quantum Control Landscapes	p. 353
4.3.9 Topology of Quantum Control Landscapes	p. 360
4.3.10 Pure-State Landscape	p. 363
4.3.11 Further on Controllability of Quantum Systems	p. 368
4.3.12 Design of Quantum Systems for Simulations	p. 371
4.3.13 Unitary Operator Landscape	p. 375
4.3.14 Global Search Algorithms	p. 383
4.3.15 Input-State Map and Its Extremals	p. 387
4.4 Open Quantum Systems	p. 392
4.4.1 Control of Open Quantum Systems	p. 392
4.4.2 Algorithm for Simulating Open Quantum Dynamics	p. 400
4.4.3 Dynamical Decoupling of Open Quantum Systems	p. 409
4.5 Discrete Control Example: Minimal Quantum Tic-Tac-Toe	p. 414
4.5.1 Minimalistic Quantization of Tic-Tac-Toe	p. 415
4.5.2 Quantum moves and winning condition	p. 416
4.5.3 Random games	p. 418
4.5.4 Deterministic games	p. 421
4.6 Biological Example: Electrical Muscular Stimulation	p. 423
4.6.1 Introduction to EMS with Diamond Medi Lift	p. 423
4.6.2 Neuro-Muscular EMS-Physiology with Diamond Medi Lift	p. 426
4.6.3 Quantum EMS-Physics with Diamond Medi Lift	p. 428
4.6.4 Quantum EMS-Control with Diamond Medi Lift	p. 436
4.6.5 EMS-Treatment for the Back-Pain with Diamond Medi Lift	p. 439
4.6.6 EMS Summary	p. 443
5 Control and Synchronization in Complex Systems and Human Crowds	p. 445
5.1 Arrays of Coupled Nonlinear Oscillators	p. 445
5.1.1 Cluster Synchrony in Systems of Coupled Oscillators	p. 446
5.1.2 Coordinated Motions on Euclidean Group SE(3) and Its Subgroups	p. 452
5.1.3 Reaction-Diffusion Systems	p. 461
5.1.4 Cellular Neural and Nonlinear Networks	p. 465
5.1.5 Ricci Flow and Reaction-Diffusion Systems	p. 471
5.2 Introduction to Crowd Dynamics	p. 484
5.2.1 Crowd Configuration Manifold M	p. 485
5.2.2 Crowd Kinematics	p. 485
5.2.3 Crowd Ricci Flow	p. 490
5.3 Group Dynamics with Psycho-Physical Conflict Behaviors	p. 492
5.3.1 A two-party crowd spatio-temporal dynamics	p. 496
5.3.2 Individual conflict-attractor dynamics	p. 499
5.3.3 Synchronized Langevin dynamics	p. 502
5.3.4 Wigner Function Description of Group Dynamics	p. 507
5.3.5 Topology of Lewinian group manifolds	p. 508
5.4 Crowd Dualities: Geometrical, Topological and Physical	p. 509
5.4.1 Geometrical Crowd-Duality Theorem	p. 509
5.4.2 Topological Crowd-Duality Theorem	p. 514
5.4.3 Physical and Global Duality of Crowd Dynamics	p. 516
5.5 Gauge-Field Dynamics of Large Human Crowds	p. 517
5.5.1 Basic topological gauge-field model	p. 519
5.5.2 Topological partition function	p. 521
5.5.3 Hodge decomposition and crowd gauge-path integral	p. 523
5.5.4 Simple HGF model	p. 524
5.5.5 More realistic HGF model	p. 525
5.6 Crowd Turbulence and Nonlinear Crowd Waves	p. 528
5.6.1 Classical Approach to Crowd Turbulence	p. 530
5.6.2 Quantum Approach to Crowd Turbulence	p. 538
5.6.3 A Variety of Crowd Waves	p. 544
5.7 Topological Panic in Crowd Behaviors	p. 551
5.7.1 Geometrical Chaos in Crowd Dynamics	p. 552
5.7.2 Topological Braiding Chaos in Crowd Dynamics	p. 554
5.7.3 Hypothetical Simulations on Topological Quantum Computers	p. 557
5.8 Nonlinear Adaptive Wave Models for Option Pricing	p. 562
5.8.1 Adaptive wave model for general option pricing	p. 564
5.8.2 Quantum wave model for low interest-rate options	p. 568
5.8.3 A new stock-market research program	p. 573
5.8.4 Conclusion	p. 573
6 Appendix	p. 575
6.1 Algebraic Preliminaries	p. 575
6.1.1 Sets, Maps and Commutative Diagrams	p. 575
6.1.2 Groups	p. 578
6.2 Manifolds and Lie Groups	p. 579
6.2.1 Calculus and Dynamics on Smooth Manifolds	p. 579
6.2.2 Lie Groups and their Lie algebras	p. 603
6.3 Lagrange Multipliers and Hessian Matrix	p. 620
6.3.1 Method of Lagrange multipliers	p. 620
6.3.2 Hessian matrix and second-derivative test	p. 621
6.4 Path Integral Quantization	p. 622
6.4.1 Feynman's Amplitude	p. 622
6.4.2 Lagrangian Action	p. 623
6.4.3 Partition Function	p. 624
6.5 Geometric Quantization	p. 625
6.5.1 Quantization of Hamiltonian Mechanics	p. 625
6.5.2 Quantization of Relativistic Hamiltonian Mechanics	p. 628
6.6 Crowd Behavior Dynamics in the Life Space Foam	p. 633
6.6.1 Life Space Foam	p. 633
6.6.2 Classical Versus Quantum Probability	p. 637
6.6.3 A Three-Step Crowd Behavior Dynamics	p. 642
6.6.4 Method of Lines for the Crowd NLS-Equations	p. 645
6.7 Braids and Entropies	p. 646
6.7.1 Knots and Braids	p. 646
6.7.2 Exponents, Dimensions and Entropies	p. 658
References	p. 663
Index	p. 707

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