New trends in control theory / Vladimir G. Ivancevic, Tijana T. Ivancevic.

Format:

Book

Author/Creator:

Ivancevic, Vladimir G.

Contributor:

Ivancevic, Tijana T.

Series:

Series on Stability, Vibration & Control of Systems: Series A

Series on stability, vibration and control of systems ; 19

Language:

English

Subjects (All):

Control theory.

Robotics--Control systems.

Robotics.

Physical Description:

1 online resource (737 p.)

Place of Publication:

Singapore : World Scientific, 2013.

Language Note:

English

Summary:

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

Contents:

Preface; Acknowledgments; Contents; 1 Introduction; 1.1 Geometrical Preliminaries; 1.1.1 Variational Method of Classical Mechanics; Lagrangian Formalism; Hamiltonian Equations; 1.1.2 Lie Algebra Mechanics; 1.1.3 Covariant Dynamics Modelling; Lagrangian Covariant Modelling; General Covariant Modelling; 1.1.4 Exterior Differential Forms; From Green to Stokes; Exterior derivative; Exterior p-forms in Rn; Stokes Theorem in Rn; Topological duality of p-forms and p-chains; Basics of De Rham theory; de Rham cohomology of a smooth manifold; 1.1.5 Hodge Theory Basics; Hodge Star Operator

Hodge Inner ProductHodge Codifferential; Hodge Laplacian; Hodge Adjoints; Hodge Decomposition Theorem; 1.1.6 Principal G-Bundles, Connections and G-Snakes; Principal G-Bundles; Connections on Principal G-Bundles; G-Snakes; Nonholonomic Connection on a principal G-bundle; 1.1.7 Wei-Norman Exponential Method; Wei-Norman Method for Riccati Equation; 1.2 Quantum Preliminaries; 1.2.1 Basic Quantum Mechanics; Quantum states and operators; Three quantum pictures; Dirac's probability amplitude and time-dependent perturbation; State-space for n non-relativistic quantum particles

1.2.2 Basic Quantum FieldsAmplitude, relativistic invariance and causality; Gauge Theories; Free and interacting field theories; Dirac's QED; Abelian Higgs Model; 1.2.3 Wigner Function Basics; 1.2.4 Path Integral Quantization; Feynman's Action-Amplitude Formalism; Correlation Functions and Generating Functional; Path-Integral QED; 1.2.5 Gauge Path-Integral via Hodge Decomposition; Functional Measure on the Space of Differential Forms; Abelian Chern-Simons Theory; 2 Basics of Classical Control Theory; 2.1 Linear Systems and Signals; 2.1.1 Laplace Transform and Transfer-Function Methods

Laplace Transforms and Transfer-Functions in MathematicaTMSolution of an Initial Value Problem; Common Responses of 2nd-Order LTI Systems; Convolution in MathematicaTM; Convolving Gaussians; 2.1.2 Fourier and Wavelet Transforms for Linear Signals; Fourier Transforms; Wavelets; Continuous Wavelet Transforms; Discrete Wavelet Transforms; DWT-Cascading and Filter Banks; Examples of DWT-Code; Wavelet-Based Multiresolution Analysis; Wavelet Series; Signal De-Noising with Wavelet Transforms; Medical Example: Analysis of Heartbeat Intervals; 2.1.3 Kalman's Modular State-Space and Filtering Methods

Basics of Kalman FilteringRadar-Tracking Problem and 1D Filters; Ordinary (Linear) Kalman Filter; Extended (Nonlinear) Kalman Filter; Sensor Fusion in Hybrid Systems; Biomechanical Examples of Kalman Filtering; Filter for Attitude Estimation in Biomechanics; Adaptive Estimation in Human Spatial Orientation; 2.1.4 Controllability of Linear Systems; Regulator Problem and the Steady State Operator; End Point Control Problem and the Adjustment Operator; Servomechanism Problem and the Corresponding Operator; Repetitive Mode Problem and the Corresponding Operator; Feedback Changes the Operator

2.1.5 Stability of Linear Systems

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

1-283-90010-6

981-4425-95-8

OCLC:

826853981