Discrete-time Stochastic Systems

Discrete-time Stochastic Systems
Author: Torsten Söderström
Publisher: Springer Science & Business Media
Total Pages: 410
Release: 2002-07-26
Genre: Mathematics
ISBN: 9781852336493

This comprehensive introduction to the estimation and control of dynamic stochastic systems provides complete derivations of key results. The second edition includes improved and updated material, and a new presentation of polynomial control and new derivation of linear-quadratic-Gaussian control.

Control and System Theory of Discrete-Time Stochastic Systems

Control and System Theory of Discrete-Time Stochastic Systems
Author: Jan H. van Schuppen
Publisher: Springer Nature
Total Pages: 940
Release: 2021-08-02
Genre: Technology & Engineering
ISBN: 3030669521

This book helps students, researchers, and practicing engineers to understand the theoretical framework of control and system theory for discrete-time stochastic systems so that they can then apply its principles to their own stochastic control systems and to the solution of control, filtering, and realization problems for such systems. Applications of the theory in the book include the control of ships, shock absorbers, traffic and communications networks, and power systems with fluctuating power flows. The focus of the book is a stochastic control system defined for a spectrum of probability distributions including Bernoulli, finite, Poisson, beta, gamma, and Gaussian distributions. The concepts of observability and controllability of a stochastic control system are defined and characterized. Each output process considered is, with respect to conditions, represented by a stochastic system called a stochastic realization. The existence of a control law is related to stochastic controllability while the existence of a filter system is related to stochastic observability. Stochastic control with partial observations is based on the existence of a stochastic realization of the filtration of the observed process.​

Mathematical Methods in Robust Control of Discrete-Time Linear Stochastic Systems

Mathematical Methods in Robust Control of Discrete-Time Linear Stochastic Systems
Author: Vasile Dragan
Publisher: Springer Science & Business Media
Total Pages: 349
Release: 2009-11-10
Genre: Mathematics
ISBN: 1441906304

In this monograph the authors develop a theory for the robust control of discrete-time stochastic systems, subjected to both independent random perturbations and to Markov chains. Such systems are widely used to provide mathematical models for real processes in fields such as aerospace engineering, communications, manufacturing, finance and economy. The theory is a continuation of the authors’ work presented in their previous book entitled "Mathematical Methods in Robust Control of Linear Stochastic Systems" published by Springer in 2006. Key features: - Provides a common unifying framework for discrete-time stochastic systems corrupted with both independent random perturbations and with Markovian jumps which are usually treated separately in the control literature; - Covers preliminary material on probability theory, independent random variables, conditional expectation and Markov chains; - Proposes new numerical algorithms to solve coupled matrix algebraic Riccati equations; - Leads the reader in a natural way to the original results through a systematic presentation; - Presents new theoretical results with detailed numerical examples. The monograph is geared to researchers and graduate students in advanced control engineering, applied mathematics, mathematical systems theory and finance. It is also accessible to undergraduate students with a fundamental knowledge in the theory of stochastic systems.

Discrete Stochastic Processes

Discrete Stochastic Processes
Author: Robert G. Gallager
Publisher: Springer Science & Business Media
Total Pages: 280
Release: 2012-12-06
Genre: Technology & Engineering
ISBN: 146152329X

Stochastic processes are found in probabilistic systems that evolve with time. Discrete stochastic processes change by only integer time steps (for some time scale), or are characterized by discrete occurrences at arbitrary times. Discrete Stochastic Processes helps the reader develop the understanding and intuition necessary to apply stochastic process theory in engineering, science and operations research. The book approaches the subject via many simple examples which build insight into the structure of stochastic processes and the general effect of these phenomena in real systems. The book presents mathematical ideas without recourse to measure theory, using only minimal mathematical analysis. In the proofs and explanations, clarity is favored over formal rigor, and simplicity over generality. Numerous examples are given to show how results fail to hold when all the conditions are not satisfied. Audience: An excellent textbook for a graduate level course in engineering and operations research. Also an invaluable reference for all those requiring a deeper understanding of the subject.

Discrete-Time Markov Jump Linear Systems

Discrete-Time Markov Jump Linear Systems
Author: O.L.V. Costa
Publisher: Springer Science & Business Media
Total Pages: 287
Release: 2006-03-30
Genre: Mathematics
ISBN: 1846280826

This will be the most up-to-date book in the area (the closest competition was published in 1990) This book takes a new slant and is in discrete rather than continuous time

Stochastic Systems

Stochastic Systems
Author: P. R. Kumar
Publisher: SIAM
Total Pages: 371
Release: 2015-12-15
Genre: Mathematics
ISBN: 1611974259

Since its origins in the 1940s, the subject of decision making under uncertainty has grown into a diversified area with application in several branches of engineering and in those areas of the social sciences concerned with policy analysis and prescription. These approaches required a computing capacity too expensive for the time, until the ability to collect and process huge quantities of data engendered an explosion of work in the area. This book provides succinct and rigorous treatment of the foundations of stochastic control; a unified approach to filtering, estimation, prediction, and stochastic and adaptive control; and the conceptual framework necessary to understand current trends in stochastic control, data mining, machine learning, and robotics.

Linear Stochastic Systems

Linear Stochastic Systems
Author: Peter E. Caines
Publisher: SIAM
Total Pages: 892
Release: 2018-06-12
Genre: Mathematics
ISBN: 1611974712

Linear Stochastic Systems, originally published in 1988, is today as comprehensive a reference to the theory of linear discrete-time-parameter systems as ever. Its most outstanding feature is the unified presentation, including both input-output and state space representations of stochastic linear systems, together with their interrelationships. The author first covers the foundations of linear stochastic systems and then continues through to more sophisticated topics including the fundamentals of stochastic processes and the construction of stochastic systems; an integrated exposition of the theories of prediction, realization (modeling), parameter estimation, and control; and a presentation of stochastic adaptive control theory. Written in a clear, concise manner and accessible to graduate students, researchers, and teachers, this classic volume also includes background material to make it self-contained and has complete proofs for all the principal results of the book. Furthermore, this edition includes many corrections of errata collected over the years.

Discrete-time Stochastic Systems

Discrete-time Stochastic Systems
Author: Torsten Söderström
Publisher: Springer Science & Business Media
Total Pages: 387
Release: 2012-12-06
Genre: Mathematics
ISBN: 1447101014

This comprehensive introduction to the estimation and control of dynamic stochastic systems provides complete derivations of key results. The second edition includes improved and updated material, and a new presentation of polynomial control and new derivation of linear-quadratic-Gaussian control.

Stochastic Discrete Event Systems

Stochastic Discrete Event Systems
Author: Armin Zimmermann
Publisher: Springer Science & Business Media
Total Pages: 393
Release: 2008-01-12
Genre: Computers
ISBN: 3540741739

Stochastic discrete-event systems (SDES) capture the randomness in choices due to activity delays and the probabilities of decisions. This book delivers a comprehensive overview on modeling with a quantitative evaluation of SDES. It presents an abstract model class for SDES as a pivotal unifying result and details important model classes. The book also includes nontrivial examples to explain real-world applications of SDES.

Stochastic Control in Discrete and Continuous Time

Stochastic Control in Discrete and Continuous Time
Author: Atle Seierstad
Publisher: Springer Science & Business Media
Total Pages: 299
Release: 2008-11-11
Genre: Mathematics
ISBN: 0387766162

This book contains an introduction to three topics in stochastic control: discrete time stochastic control, i. e. , stochastic dynamic programming (Chapter 1), piecewise - terministic control problems (Chapter 3), and control of Ito diffusions (Chapter 4). The chapters include treatments of optimal stopping problems. An Appendix - calls material from elementary probability theory and gives heuristic explanations of certain more advanced tools in probability theory. The book will hopefully be of interest to students in several ?elds: economics, engineering, operations research, ?nance, business, mathematics. In economics and business administration, graduate students should readily be able to read it, and the mathematical level can be suitable for advanced undergraduates in mathem- ics and science. The prerequisites for reading the book are only a calculus course and a course in elementary probability. (Certain technical comments may demand a slightly better background. ) As this book perhaps (and hopefully) will be read by readers with widely diff- ing backgrounds, some general advice may be useful: Don’t be put off if paragraphs, comments, or remarks contain material of a seemingly more technical nature that you don’t understand. Just skip such material and continue reading, it will surely not be needed in order to understand the main ideas and results. The presentation avoids the use of measure theory.