Randomized Algorithms for Analysis and Control of Uncertain Systems (Communications and Control Engineering)

Book Description

The presence of uncertainty in a system description has always been a critical issue in control. Moving on from earlier stochastic and robust control paradigms, the main objective of this book is to introduce the reader to the fundamentals of probabilistic methods in the analysis and design of uncertain systems. Using so-called "randomized algorithms", this emerging area of research guarantees a reduction in the computational complexity of classical robust control algorithms and in the conservativeness of methods like H-infinity control.

Features:

• self-contained treatment explaining randomized algorithms from their genesis in the principles of probability theory to their use for robust analysis and controller synthesis;

• comprehensive treatment of sample generation, including consideration of the difficulties involved in obtaining independent and identically distributed samples;

• applications of randomized algorithms in congestion control of high-speed communications networks and the stability of quantized sampled-data systems.

Randomized Algorithms for Analysis and Control of Uncertain Systems will be of certain interest to control theorists concerned with robust and optimal control techniques and to all control engineers dealing with system uncertainties.

The present book is a very timely contribution to the literature. I have no hesitation in asserting that it will remain a widely cited reference work for many years.

M. Vidyasagar

Random Iterative Models (Stochastic Modelling and Applied Probability)

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Random Iterative Models (Stochastic Modelling and Applied Probability)
Marie Duflo
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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ASIN: 3540571000

Book Description

The recent development of computation and automation has lead to quick advances in the theory and practice of recursive methods for stabilization, identification and control of complex stochastic models (guiding a rocket or a plane, organizing multiaccess broadcast channels, self-learning of neural networks ...). This book provides an up-to-date view of a wide range of those methods: stochastic approximation, linear and non-linear models, controlled Markov chains, estimation and adaptive control, learning ...Mathematicians (researchers and also students) and engineers will find here a self-contained account of many approaches to those theories.

Stochastic Approximation and Its Application (Nonconvex Optimization and Its Applications)

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Stochastic Approximation and Its Application (Nonconvex Optimization and Its Applications)
Han-Fu Chen
Manufacturer: Springer
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Binding: Hardcover

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ASIN: 1402008066

Book Description

This book presents the recent development of stochastic approximation algorithms with expanding truncations based on the TS (trajectory-subsequence) method, a newly developed method for convergence analysis. This approach is so powerful that conditions used for guaranteeing convergence have been considerably weakened in comparison with those applied in the classical probability and ODE methods. The general convergence theorem is presented for sample paths and is proved in a purely deterministic way. The sample-path description of theorems is particularly convenient for applications. Convergence theory takes both observation noise and structural error of the regression function into consideration. Convergence rates, asymptotic normality and other asymptotic properties are presented as well. Applications of the developed theory to global optimization, blind channel identification, adaptive filtering, system parameter identification, adaptive stabilization and other problems arising from engineering fields are demonstrated.
Audience: Researchers and students of both graduate and undergraduate levels in systems and control, optimization, signal processing, communication and statistics.

Linear Stochastic Control Systems (Probability and Stochastics)

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Linear Stochastic Control Systems (Probability and Stochastics)
Goong Chen , Guanrong Chen , and Shih-Hsun Hsu
Manufacturer: CRC
ProductGroup: Book
Binding: Hardcover

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ASIN: 0849380758

Book Description

Linear Stochastic Control Systems presents a thorough description of the mathematical theory and fundamental principles of linear stochastic control systems. Both continuous-time and discrete-time systems are thoroughly covered. Reviews of the modern probability and random processes theories and the Itô stochastic differential equations are provided. Discrete-time stochastic systems theory, optimal estimation and Kalman filtering, and optimal stochastic control theory are studied in detail. A modern treatment of these same topics for continuous-time stochastic control systems is included. The text is written in an easy-to-understand style, and the reader needs only to have a background of elementary real analysis and linear deterministic systems theory to comprehend the subject matter. This graduate textbook is also suitable for self-study, professional training, and as a handy research reference. Linear Stochastic Control Systems is self-contained and provides a step-by-step development of the theory, with many illustrative examples, exercises, and engineering applications.

H-infinity Control and Estimation of State-multiplicative Linear Systems (Lecture Notes in Control and Information Sciences)

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H-infinity Control and Estimation of State-multiplicative Linear Systems (Lecture Notes in Control and Information Sciences)
Eli Gershon , Uri Shaked , and Isaac Yaesh
Manufacturer: Springer
ProductGroup: Book
Binding: Paperback

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ASIN: 1852339977

Book Description

Control and estimation of linear systems with state-multiplicative noise in the H-infinity setting is covered in this monograph. Multiplicative noise appears in systems where the process or measurement noise levels depend on the system state vector. Such systems are relevant when a gain-scheduled controller utilizes a noisy gain-scheduling parameter or when the noise level depends on one or more of the states; the latter is encountered, for example, in radar measurements where larger ranges involve higher noise level. The last decade has witnessed a resurgence of interest in the study of these systems, which constitute a special class of nonlinear systems, mainly in the field of H-infinity control. H-infinity Control and Estimation of State-multiplicative Linear Systems embodies a comprehensive survey of the relevant literature with basic problems being formulated and solved by applying various techniques including game theory, linear matrix inequalities and Lyapunov parameter-dependent functions. Topics covered include: practical problems in which state-multiplicative noise has to be dealt with; convex H2 and H-infinity norms analysis of systems with multiplicative noise; state feedback control and state estimation of systems with multiplicative noise; dynamic and static output feedback of stochastic bilinear systems; tracking controllers for stochastic bilinear systems utilizing preview information. Various examples which demonstrate the applicability of the theory to practical control engineering problems are considered; two such examples are taken from the aerospace and guidance control areas.

Dynamic Stochastic Optimization (Lecture Notes in Economics and Mathematical Systems)

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Dynamic Stochastic Optimization (Lecture Notes in Economics and Mathematical Systems)

Manufacturer: Springer
ProductGroup: Book
Binding: Paperback

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ASIN: 3540405062

Book Description

This volume considers optimal stochastic decision processes from the viewpoint of stochastic programming. It focuses on theoretical properties and on approximate or numerical solution techniques for time-dependent optimization problems with random parameters (multistage stochastic programs, optimal stochastic decision processes). Methods for finding approximate solutions of probabilistic and expected cost based deterministic substitute problems are presented. Besides theoretical and numerical considerations, the proceedings volume contains selected refereed papers on many practical applications to economics and engineering: risk, risk management, portfolio management, finance, insurance-matters and control of robots.

Stochastic Switching Systems: Analysis and Design (Control Engineering)

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Stochastic Switching Systems: Analysis and Design (Control Engineering)
El-Kébir Boukas
Manufacturer: Birkhäuser Boston
ProductGroup: Book
Binding: Hardcover

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ASIN: 0817637826

Book Description

Stochastic switching systems represent an interesting class, which can be used to model a variety of systems having abrupt random changes in their dynamics. Such systems may be found in the fields of manufacturing, communications, aerospace, power, and economics.

This work presents stochastic switching systems and provides up-to-date methods and techniques for the analysis and design of various control systems with or without uncertainties. An introductory chapter highlights basic concepts and practical models, which are then used to solve more advanced problems throughout the book. Included are many numerical examples as well as LMI analysis methods and design approaches to supplement the developed results.

Specific topics covered include:

* The stochastic stability problem and its robustness.

* The stabilization problem; different controllers such as the state feedback, output feedback, and observer-based output feedback are designed for nominal and uncertain systems using LMI conditions.

* Systems with external disturbances; different approaches are developed to reject the external disturbances.

* The filtering problem for the class of systems with Markovian jump parameters; Kalman and H-infinity filtering problems are treated and LMI conditions are developed to synthesize the gains of these filters.

* Systems with singular Markovian jump parameters.

Stochastic Switching Systems may be used as a supplementary textbook for graduate-level engineering courses, or as a reference for control engineers, graduate students, and researchers in systems and control. Prerequisites include elementary courses in matrix theory, probability, optimization techniques, and control systems theory.

Introduction to Mathematical Systems Theory: Linear Systems, Identification and Control

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Introduction to Mathematical Systems Theory: Linear Systems, Identification and Control
Christiaan Heij , André Ran , and Freek van Schagen
Manufacturer: Birkhäuser Basel
ProductGroup: Book
Binding: Paperback

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ASIN: 3764375485

Discrete-Time Markov Jump Linear Systems (Probability and its Applications)

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Discrete-Time Markov Jump Linear Systems (Probability and its Applications)
O.L.V. Costa , M.D. Fragoso , and R.P. Marques
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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ASIN: 1852337613

Book Description

Safety critical and high-integrity systems, such as industrial plants and economic systems can be subject to abrupt changes - for instance due to component or interconnection failure, and sudden environment changes etc.

Combining probability and operator theory, Discrete-Time Markov Jump Linear Systems provides a unified and rigorous treatment of recent results for the control theory of discrete jump linear systems, which are used in these areas of application.

The book is designed for experts in linear systems with Markov jump parameters, but is also of interest for specialists in stochastic control since it presents stochastic control problems for which an explicit solution is possible - making the book suitable for course use.

From the reviews:

"This text is very well written...it may prove valuable to those who work in the area, are at home with its mathematics, and are interested in stability of linear systems, optimal control, and filtering." Journal of the American Statistical Association, December 2005

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Discrete-time Stochastic Systems
Torsten Söderström
Manufacturer: Springer
ProductGroup: Book
Binding: Paperback

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Introduction to Stochastic Control Theory

ASIN: 1852336498

Book Description

Discrete-time Stochastic Systems gives a comprehensive introduction to the estimation and control of dynamic stochastic systems and provides complete derivations of key results such as the basic relations for Wiener filtering. The book covers both state-space methods and those based on the polynomial approach. Similarities and differences between these approaches are highlighted. Some non-linear aspects of stochastic systems (such as the bispectrum and extended Kalman filter) are also introduced and analysed. The books chief features are as follows: inclusion of the polynomial approach provides alternative and simpler computational methods than simple reliance on state-space methods; algorithms for analysis and design of stochastic systems allow for ease of implementation and experimentation by the reader; the highlighting of spectral factorization gives appropriate emphasis to this key concept often overlooked in the literature; explicit solutions of Wiener problems are handy schemes, well suited for computations compared with more commonly available but abstract formulations; complex-valued models that are directly applicable to many problems in signal processing and communications. Changes in the second edition include: additional information covering spectral factorisation and the innovations form; the chapter on optimal estimation being completely rewritten to focus on a posterior estimates rather than maximum likelihood; new material on fixed lag smoothing and algorithms for solving Riccati equations are improved and more up to date; new presentation of polynomial control and new derivation of linear-quadratic-Gaussian control. Discrete-time Stochastic Systems is primarily of benefit to students taking M.Sc. courses in stochastic estimation and control, electronic engineering and signal processing but may also be of assistance for self study and as a reference.

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