Springer Tracts in Modern Physics

Concepts, Tools, and Applications

By: Michael Schulz

Write A Review

Hardcover | 8 December 2005

At a Glance

Hardcover
324 Pages

Dimensions(cm)
23.5 x 16.51 x 1.91

Hardcover

$249.00

or 4 interest-free payments of $62.25 with

Ships in 5 to 7 business days

This book provides an introduction to the analysis and the control mechanism of physical, chemical, biological, technological and economic models and their nonequilibrium evolution dynamics. Strong emphasis is placed on the foundation of variational principles, evolution and control equations, numerical methods, statistical concepts and techniques for solving or estimation of stochastic control problems for systems with a high degree of complexity. In particular, the central aim of this book is developing a synergetic connection between theoretical concepts and real applications. This book is a modern introduction and a helpful tool for researchers as well as for graduate students interested in econophysics and related topics.

Industry Reviews

From the reviews: "The monograph under review introduces control-theoretic issues which arise in, primarily, physics-related areas. The texts is, in fact, addressed to the physics community, and this is manifested in several ways. First, the style of presentation ... . Secondly, the terminology ... . Content-wise the monograph offers a variety of topics, more diverse ... collected according to their physical context. ... All in all, a reader ... will find here a variety of issues, lively explanations and useful references to the literature." (Zvi Artstein, Mathematical Reviews, Issue 2007 c)

Shipping

	Standard Shipping	Express Shipping
Metro postcodes:	$9.99	$14.95
Regional postcodes:	$9.99	$14.95
Rural postcodes:	$9.99	$14.95

Orders over $89.00 qualify for free shipping.

How to return your order

At Booktopia, we offer hassle-free returns in accordance with our returns policy. If you wish to return an item, please get in touch with Booktopia Customer Care.

Additional postage charges may be applicable.

Defective items

If there is a problem with any of the items received for your order then the Booktopia Customer Care team is ready to assist you.

For more info please visit our Help Centre.

Introduction	p. 1
The Aim of Control Theory	p. 1
Dynamic State of Classical Mechanical Systems	p. 3
Dynamic State of Complex Systems	p. 6
What Is a Complex System?	p. 6
Relevant and Irrelevant Degrees of Freedom	p. 9
Quasi-Deterministic Versus Quasi-Stochastic Evolution	p. 10
The Physical Approach to Control Theory	p. 13
References	p. 14
Deterministic Control Theory	p. 17
Introduction: The Brachistochrone Problem	p. 17
The Deterministic Control Problem	p. 19
Functionals, Constraints, and Boundary Conditions	p. 19
Weak and Strong Minima	p. 20
The Simplest Control Problem: Classical Mechanics	p. 22
Euler-Lagrange Equations	p. 22
Optimum Criterion	p. 24
One-Dimensional Systems	p. 30
General Optimum Control Problem	p. 33
Lagrange Approach	p. 33
Hamilton Approach	p. 40
Pontryagin's Maximum Principle	p. 42
Applications of the Maximum Principle	p. 45
Controlled Molecular Dynamic Simulations	p. 53
The Hamilton-Jacobi Equation	p. 55
References	p. 59
Linear Quadratic Problems	p. 61
Introduction to Linear Quadratic Problems	p. 61
Motivation	p. 61
The Performance Functional	p. 62
Stability Analysis	p. 63
The General Solution of Linear Quadratic Problems	p. 71
Extensions and Applications	p. 73
Modifications of the Performance	p. 73
Inhomogeneous Linear Evolution Equations	p. 75
Scalar Problems	p. 75
The Optimal Regulator	p. 77
Algebraic Ricatti Equation	p. 77
Stability of Optimal Regulators	p. 79
Control of Linear Oscillations and Relaxations	p. 81
Integral Representation of State Dynamics	p. 81
Optimal Control of Generalized Linear Evolution Equations	p. 85
Perturbation Theory for Weakly Nonlinear Dynamics	p. 88
References	p. 90
Control of Fields	p. 93
Field Equations	p. 93
Classical Field Theory	p. 93
Hydrodynamic Field Equations	p. 99
Other Field Equations	p. 101
Control by External Sources	p. 103
General Aspects	p. 103
Control Without Spatial Boundaries	p. 104
Passive Boundary Conditions	p. 114
Control via Boundary Conditions	p. 116
References	p. 118
Chaos Control	p. 123
Characterization of Trajectories in the Phase Space	p. 123
General Problems	p. 123
Conservative Hamiltonian Systems	p. 124
Nonconservative Systems	p. 126
Time-Discrete Chaos Control	p. 128
Time Continuous Control Versus Time Discrete Control	p. 128
Chaotic Behavior of Time Discrete Systems	p. 132
Control of Time Discrete Equations	p. 135
Reachability and Stabilizability	p. 137
Observability	p. 140
Time-Continuous Chaos Control	p. 141
Delayed Feedback Control	p. 141
Synchronization	p. 144
References	p. 146
Nonequilibrium Statistical Physics	p. 149
Statistical Approach to Phase Space Dynamics	p. 149
The Probability Distribution	p. 149
The Liouville Equation	p. 152
Generalized Rate Equations	p. 153
Probability Distribution of Relevant Quantities	p. 153
The Formal Solution of the Liouville Equation	p. 155
The Nakajima-Zwanzig Equation	p. 156
Notation of Probability Theory	p. 161
Measures of Central Tendency	p. 161
Measure of Fluctuations around the Central Tendency	p. 162
Moments and Characteristic Functions	p. 162
Cumulants	p. 163
Combined Probabilities	p. 164
Conditional Probability	p. 164
Joint Probability	p. 165
Markov Approximation	p. 167
Generalized Fokker-Planck Equation	p. 169
Differential Chapman-Kolmogorov Equation	p. 169
Deterministic Processes	p. 173
Markov Diffusion Processes	p. 174
Jump Processes	p. 175
Correlation and Stationarity	p. 176
Stationarity	p. 176
Correlation	p. 177
Spectra	p. 178
Stochastic Equations of Motions	p. 179
The Mori-Zwanzig Equation	p. 179
Separation of Time Scales	p. 182
Wiener Process	p. 183
Stochastic Differential Equations	p. 185
Ito's Formula and Fokker-Planck Equation	p. 189
References	p. 191
Optimal Control of Stochastic Processes	p. 193
Markov Diffusion Processes under Control	p. 193
Information Level and Control Mechanisms	p. 193
Path Integrals	p. 194
Performance	p. 197
Optimal Open Loop Control	p. 199
Mean Performance	p. 199
Tree Approximation	p. 201
Feedback Control	p. 204
The Control Equation	p. 204
Linear Quadratic Problems	p. 210
References	p. 211
Filters and Predictors	p. 213
Partial Uncertainty of Controlled Systems	p. 213
Gaussian Processes	p. 215
The Central Limit Theorem	p. 215
Convergence Problems	p. 220
Lévy Processes	p. 223
Form-Stable Limit Distributions	p. 223
Convergence to Stable Lévy Distributions	p. 226
Truncated Lévy Distributions	p. 227
Rare Events	p. 228
The Cramér Theorem	p. 228
Extreme Fluctuations	p. 230
Kalman Filter	p. 232
Linear Quadratic Problems with Gaussian Noise	p. 232
Estimation of the System State	p. 232
Ljapunov Differential Equation	p. 237
Optimal Control Problem for Kalman Filters	p. 239
Filters and Predictors	p. 243
General Filter Concepts	p. 243
Wiener Filters	p. 244
Estimation of the System Dynamics	p. 245
Regression and Autoregression	p. 246
The Bayesian Concept	p. 249
Neural Networks	p. 251
References	p. 261
Game Theory	p. 265
Unpredictable Systems	p. 265
Optimal Control and Decision Theory	p. 267
Nondeterministic and Probabilistic Regime	p. 267
Strategies	p. 269
Zero-Sum Games	p. 271
Two-Player Games	p. 271
Deterministic Strategy	p. 272
Random Strategy	p. 273
Nonzero-Sum Games	p. 274
Nash Equilibrium	p. 274
Random Nash Equilibria	p. 276
References	p. 276
Optimization Problems	p. 279
Notations of Optimization Theory	p. 279
Introduction	p. 279
Convex Objects	p. 280
Optimization Methods	p. 282
Extremal Solutions Without Constraints	p. 282
Extremal Solutions with Constraints	p. 285
Linear Programming	p. 286
Combinatorial Optimization Problems	p. 287
Evolution Strategies	p. 289
References	p. 292
Table of Contents provided by Publisher. All Rights Reserved.

Springer Tracts in Modern Physics

Concepts, Tools, and Applications

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

More in Mathematical Physics

High Order Methods and Applications in Computational Mechanics

Fluid Mechanics and Its Applications

Quantum Physics For Dummies

For Dummies

The Delicate Art of Brute Force

How to Compute It When You Can't Solve It

A Physicist's Introduction to Algebraic Structures

Vector Spaces, Groups, Topological Spaces and More

Abstract Cauchy Problems

Three Approaches

Kirchhoff Equations

A Variational Approach

Noncommutative measures and Orlicz Spaces, with Applications to Quantum Physic

Oxford Graduate Texts in Mathematics

Computational Problems for Physics

With Guided Solutions Using Python

Computational Problems for Physics

With Guided Solutions Using Python

Mathematical Methods for Physics and Engineering

Practical Applications

Mathematical Methods for Physics and Engineering

Practical Applications

Mathematical Methods using Python

Applications in Physics and Engineering

Mathematical Modelling for Engineering and Physical Applications

Practical Examples and Case Studies

Darboux Transformation of Nonlinear Schrodinger Equations

A Guide and a Tutorial

Problems in Quantum Mechanics and Field Theory with Mathematical Modelling

Is Mind Just a Computation?

How Computer Science Dispels the Myths of the Age of AI

Elements of Mathematical Methods for Physics

Proofs and Logical Arguments Supporting the Foundational Laws of Physics

A Handy Guide for Students and Scientists

Computational Modelling with Single Prompts

Series in Computational Physics

The Physics and Mathematics of MRI

Imaging in Medical Diagnosis and Therapy

The Physics and Mathematics of MRI

Imaging in Medical Diagnosis and Therapy

Gauge Fields, Knots And Gravity

Series on Knots & Everything

Mathematical Advances in Theoretical Chemistry

Developments in Physical & Theoretical Chemistry

Scattering of Waves

Theory and Applications

This product is categorised by