Mathematical Methods In Robust Control Of Discrete Time Linear Stochastic Systems

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.

This second edition of Mathematical Methods in the Robust Control of Linear Stochastic Systems includes a large number of recent results in the control of linear stochastic systems. More specifically, the new results presented are: - A unified and abstract framework for Riccati type equations arising in the stochastic control - Stability and control problems for systems perturbed by homogeneous Markov processes with infinite number of states - Mixed H2 / H∞ control problem and numerical procedures - Linear differential equations with positive evolution on ordered Banach spaces with applications for stochastic systems including both multiplicative white noise and Markovian jumps represented by a Markov chain with countable infinite set of states - Kalman filtering for stochastic systems subject both to state dependent noise and Markovian jumps - H∞ reduced order filters for stochastic systems The book will appeal to graduate students, researchers in advanced control engineering, finance, mathematical systems theory, applied probability and stochastic processes, and numerical analysis. From Reviews of the First Edition: This book is concerned with robust control of stochastic systems. One of the main features is its coverage of jump Markovian systems. ... Overall, this book presents results taking into consideration both white noise and Markov chain perturbations. It is clearly written and should be useful for people working in applied mathematics and in control and systems theory. The references cited provide further reading sources. (George Yin, Mathematical Reviews, Issue 2007 m) This book considers linear time varying stochastic systems, subjected to white noise disturbances and system parameter Markovian jumping, in the context of optimal control ... robust stabilization, and disturbance attenuation. ... The material presented in the book is organized in seven chapters. ... The book is very well written and organized. ... is a valuable reference for all researchers and graduate students in applied mathematics and control engineering interested in linear stochastic time varying control systems with Markovian parameter jumping and white noise disturbances. (Zoran Gajic, SIAM Review, Vol. 49 (3), 2007)

The H∞ control has been one of the important robust control approaches since the 1980s. This book extends the area to nonlinear stochastic H2/H∞ control, and studies more complex and practically useful mixed H2/H∞ controller synthesis rather than the pure H∞ control. Different from the commonly used convex optimization method, this book applies the Nash game approach to give necessary and sufficient conditions for the existence and uniqueness of the mixed H2/H∞ control. Researchers will benefit from our detailed exposition of the stochastic mixed H2/H∞ control theory, while practitioners can apply our efficient algorithms to address their practical problems.

This book constitutes the proceedings of the 19th Chinese Intelligent Systems Conference, CISC 2023, which was held during October 14–15, 2023, in Ningbo, Zhejiang, China. The book focuses on new theoretical results and techniques in the field of intelligent systems and control. This is achieved by providing in-depth studies of a number of important topics such as multi-agent systems, complex networks, intelligent robots, complex systems theory and swarm behavior, event-driven and data-driven control, robust and adaptive control, big data and brain science, process control, intelligent sensors and detection technology, deep learning and learning control, navigation and control of aerial vehicles, and so on. The book is particularly suitable for readers interested in learning intelligent systems and control and artificial intelligence. The book can benefit researchers, engineers and graduate students.

This book provides an introduction to the theory of linear systems and control for students in business mathematics, econometrics, computer science, and engineering. The focus is on discrete time systems, which are the most relevant in business applications, as opposed to continuous time systems, requiring less mathematical preliminaries. The subjects treated are among the central topics of deterministic linear system theory: controllability, observability, realization theory, stability and stabilization by feedback, LQ-optimal control theory. Kalman filtering and LQC-control of stochastic systems are also discussed, as are modeling, time series analysis and model specification, along with model validation. This second edition has been updated and slightly expanded. In addition, supplementary material containing the exercises is now available on the Springer Link's book website.

This book is a collection of thoroughly refereed papers presented at the 27th IFIP TC 7 Conference on System Modeling and Optimization, held in Sophia Antipolis, France, in June/July 2015. The 48 revised papers were carefully reviewed and selected from numerous submissions. They cover the latest progress in their respective areas and encompass broad aspects of system modeling and optimiza-tion, such as modeling and analysis of systems governed by Partial Differential Equations (PDEs) or Ordinary Differential Equations (ODEs), control of PDEs/ODEs, nonlinear optimization, stochastic optimization, multi-objective optimization, combinatorial optimization, industrial applications, and numericsof PDEs.

The H∞ control has been one of the important robust control approaches since the 1980s. This book extends the area to nonlinear stochastic H2/H∞ control, and studies more complex and practically useful mixed H2/H∞ controller synthesis rather than the pure H∞ control. Different from the commonly used convex optimization method, this book applies the Nash game approach to give necessary and sufficient conditions for the existence and uniqueness of the mixed H2/H∞ control. Researchers will benefit from our detailed exposition of the stochastic mixed H2/H∞ control theory, while practitioners can apply our efficient algorithms to address their practical problems.

The aim of this Special Issue of Mathematics is to commemorate the outstanding Russian mathematician Vladimir Zolotarev, whose 90th birthday will be celebrated on February 27th, 2021. The present Special Issue contains a collection of new papers by participants in sessions of the International Seminar on Stability Problems for Stochastic Models founded by Zolotarev. Along with research in probability distributions theory, limit theorems of probability theory, stochastic processes, mathematical statistics, and queuing theory, this collection contains papers dealing with applications of stochastic models in modeling of pension schemes, modeling of extreme precipitation, construction of statistical indicators of scientific publication importance, and other fields.