Rational Matrix Equations In Stochastic Control

Author : Tobias Damm
Publisher : Springer
Page : 200 pages
File Size : 50,9 Mb
Release : 2014-10-08
Category : Mathematics
ISBN : 366219483X

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Rational Matrix Equations in Stochastic Control by Tobias Damm Pdf

This book is the first comprehensive treatment of rational matrix equations in stochastic systems, including various aspects of the field, previously unpublished results and explicit examples. Topics include modelling with stochastic differential equations, stochastic stability, reformulation of stochastic control problems, analysis of the rational matrix equation and numerical solutions. Primarily a survey in character, this monograph is intended for researchers, graduate students and engineers in control theory and applied linear algebra.

Author : Tobias Damm
Publisher : Springer Science & Business Media
Page : 228 pages
File Size : 50,9 Mb
Release : 2004-01-23
Category : Mathematics
ISBN : 3540205160

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Rational Matrix Equations in Stochastic Control by Tobias Damm Pdf

This book is the first comprehensive treatment of rational matrix equations in stochastic systems, including various aspects of the field, previously unpublished results and explicit examples. Topics include modelling with stochastic differential equations, stochastic stability, reformulation of stochastic control problems, analysis of the rational matrix equation and numerical solutions. Primarily a survey in character, this monograph is intended for researchers, graduate students and engineers in control theory and applied linear algebra.

Author : Vasile Dragan,Toader Morozan,Adrian-Mihail Stoica
Publisher : Springer Science & Business Media
Page : 320 pages
File Size : 46,7 Mb
Release : 2007-02-03
Category : Science
ISBN : 9780387359243

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Mathematical Methods in Robust Control of Linear Stochastic Systems by Vasile Dragan,Toader Morozan,Adrian-Mihail Stoica Pdf

The book covers the necessary pre-requisites from probability theory, stochastic processes, stochastic integrals and stochastic differential equations. It includes detailed treatment of the fundamental properties of stochastic systems subjected both to multiplicative white noise and to jump Markovian perturbations. Systematic presentation leads the reader in a natural way to the original results. New theoretical results accompanied by detailed numerical examples, and the book proposes new numerical algorithms to solve coupled matrix algebraic Riccati equations.

Author : Viorel Barbu,Irena Lasiecka,Dan Tiba,Constantin Varsan
Publisher : Springer
Page : 445 pages
File Size : 53,9 Mb
Release : 2013-06-05
Category : Mathematics
ISBN : 9780387356907

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Analysis and Optimization of Differential Systems by Viorel Barbu,Irena Lasiecka,Dan Tiba,Constantin Varsan Pdf

Analysis and Optimization of Differential Systems focuses on the qualitative aspects of deterministic and stochastic differential equations. Areas covered include: Ordinary and partial differential systems; Optimal control of deterministic and stochastic evolution equations; Control theory of Partial Differential Equations (PDE's); Optimization methods in PDE's with numerous applications to mechanics and physics; Inverse problems; Stability theory; Abstract optimization problems; Calculus of variations; Numerical treatment of solutions to differential equations and related optimization problems. These research fields are under very active development and the present volume should be of interest to students and researchers working in applied mathematics or in system engineering. This volume contains selected contributions presented during the International Working Conference on Analysis and Optimization of Differential Systems, which was sponsored by the International Federation for Information Processing (IFIP) and held in Constanta, Romania in September 2002. Among the aims of this conference was the creation of new international contacts and collaborations, taking advantage of the new developments in Eastern Europe, particularly in Romania. The conference benefited from the support of the European Union via the EURROMMAT program.

Author : Goong Chen,Guanrong Chen,Shih-Hsun Hsu
Publisher : CRC Press
Page : 404 pages
File Size : 49,9 Mb
Release : 1995-07-12
Category : Business & Economics
ISBN : 0849380758

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Linear Stochastic Control Systems by Goong Chen,Guanrong Chen,Shih-Hsun Hsu Pdf

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.

Author : Rafael Bru,Sergio Romero-Vivó
Publisher : Springer Science & Business Media
Page : 385 pages
File Size : 48,7 Mb
Release : 2009-08-26
Category : Technology & Engineering
ISBN : 9783642028939

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Positive Systems by Rafael Bru,Sergio Romero-Vivó Pdf

This volume contains the proceedings of the "Third Multidisciplinary Symposium on Positive Systems: Theory and Applications (POSTA09)" held in Valencia, Spain, September 2–4, 2009. This is the only world congress whose main topic is focused on this field.

Author : Hisham Abou-Kandil,Gerhard Freiling,Vlad Ionescu,Gerhard Jank
Publisher : Birkhäuser
Page : 584 pages
File Size : 46,9 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783034880817

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Matrix Riccati Equations in Control and Systems Theory by Hisham Abou-Kandil,Gerhard Freiling,Vlad Ionescu,Gerhard Jank Pdf

The authors present the theory of symmetric (Hermitian) matrix Riccati equations and contribute to the development of the theory of non-symmetric Riccati equations as well as to certain classes of coupled and generalized Riccati equations occurring in differential games and stochastic control. The volume offers a complete treatment of generalized and coupled Riccati equations. It deals with differential, discrete-time, algebraic or periodic symmetric and non-symmetric equations, with special emphasis on those equations appearing in control and systems theory. Extensions to Riccati theory allow to tackle robust control problems in a unified approach. The book makes available classical and recent results to engineers and mathematicians alike. It is accessible to graduate students in mathematics, applied mathematics, control engineering, physics or economics. Researchers working in any of the fields where Riccati equations are used can find the main results with the proper mathematical background.

Author : Jingrui Sun,Jiongmin Yong
Publisher : Springer Nature
Page : 129 pages
File Size : 49,6 Mb
Release : 2020-06-29
Category : Mathematics
ISBN : 9783030209223

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Stochastic Linear-Quadratic Optimal Control Theory: Open-Loop and Closed-Loop Solutions by Jingrui Sun,Jiongmin Yong Pdf

This book gathers the most essential results, including recent ones, on linear-quadratic optimal control problems, which represent an important aspect of stochastic control. It presents the results in the context of finite and infinite horizon problems, and discusses a number of new and interesting issues. Further, it precisely identifies, for the first time, the interconnections between three well-known, relevant issues – the existence of optimal controls, solvability of the optimality system, and solvability of the associated Riccati equation. Although the content is largely self-contained, readers should have a basic grasp of linear algebra, functional analysis and stochastic ordinary differential equations. The book is mainly intended for senior undergraduate and graduate students majoring in applied mathematics who are interested in stochastic control theory. However, it will also appeal to researchers in other related areas, such as engineering, management, finance/economics and the social sciences.

Author : Weihai Zhang,Lihua Xie,Bor-Sen Chen
Publisher : CRC Press
Page : 421 pages
File Size : 54,6 Mb
Release : 2017-08-07
Category : Computers
ISBN : 9781351643979

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Stochastic H2/H ∞ Control: A Nash Game Approach by Weihai Zhang,Lihua Xie,Bor-Sen Chen Pdf

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.

Author : Stephen Barnett
Publisher : Unknown
Page : 216 pages
File Size : 41,8 Mb
Release : 1984
Category : Mathematics
ISBN : STANFORD:36105032825643

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Matrices in Control Theory by Stephen Barnett Pdf

Author : Oswaldo Luiz do Valle Costa,Marcelo D. Fragoso,Marcos G. Todorov
Publisher : Springer Science & Business Media
Page : 295 pages
File Size : 50,8 Mb
Release : 2012-12-18
Category : Mathematics
ISBN : 9783642341007

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Continuous-Time Markov Jump Linear Systems by Oswaldo Luiz do Valle Costa,Marcelo D. Fragoso,Marcos G. Todorov Pdf

It has been widely recognized nowadays the importance of introducing mathematical models that take into account possible sudden changes in the dynamical behavior of a high-integrity systems or a safety-critical system. Such systems can be found in aircraft control, nuclear power stations, robotic manipulator systems, integrated communication networks and large-scale flexible structures for space stations, and are inherently vulnerable to abrupt changes in their structures caused by component or interconnection failures. In this regard, a particularly interesting class of models is the so-called Markov jump linear systems (MJLS), which have been used in numerous applications including robotics, economics and wireless communication. Combining probability and operator theory, the present volume provides a unified and rigorous treatment of recent results in control theory of continuous-time MJLS. This unique approach is of great interest to experts working in the field of linear systems with Markovian jump parameters or in stochastic control. The volume focuses on one of the few cases of stochastic control problems with an actual explicit solution and offers material well-suited to coursework, introducing students to an interesting and active research area. The book is addressed to researchers working in control and signal processing engineering. Prerequisites include a solid background in classical linear control theory, basic familiarity with continuous-time Markov chains and probability theory, and some elementary knowledge of operator theory. ​

Author : Peter Benner,Albert Cohen,Mario Ohlberger,Karen Willcox
Publisher : SIAM
Page : 412 pages
File Size : 46,9 Mb
Release : 2017-07-06
Category : Science
ISBN : 9781611974829

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Model Reduction and Approximation by Peter Benner,Albert Cohen,Mario Ohlberger,Karen Willcox Pdf

Many physical, chemical, biomedical, and technical processes can be described by partial differential equations or dynamical systems. In spite of increasing computational capacities, many problems are of such high complexity that they are solvable only with severe simplifications, and the design of efficient numerical schemes remains a central research challenge. This book presents a tutorial introduction to recent developments in mathematical methods for model reduction and approximation of complex systems. Model Reduction and Approximation: Theory and Algorithms contains three parts that cover (I) sampling-based methods, such as the reduced basis method and proper orthogonal decomposition, (II) approximation of high-dimensional problems by low-rank tensor techniques, and (III) system-theoretic methods, such as balanced truncation, interpolatory methods, and the Loewner framework. It is tutorial in nature, giving an accessible introduction to state-of-the-art model reduction and approximation methods. It also covers a wide range of methods drawn from typically distinct communities (sampling based, tensor based, system-theoretic).?? This book is intended for researchers interested in model reduction and approximation, particularly graduate students and young researchers.

Author : Giorgio Fabbri,Fausto Gozzi,Andrzej Święch
Publisher : Springer
Page : 916 pages
File Size : 44,8 Mb
Release : 2017-06-22
Category : Mathematics
ISBN : 9783319530673

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Stochastic Optimal Control in Infinite Dimension by Giorgio Fabbri,Fausto Gozzi,Andrzej Święch Pdf

Providing an introduction to stochastic optimal control in infinite dimension, this book gives a complete account of the theory of second-order HJB equations in infinite-dimensional Hilbert spaces, focusing on its applicability to associated stochastic optimal control problems. It features a general introduction to optimal stochastic control, including basic results (e.g. the dynamic programming principle) with proofs, and provides examples of applications. A complete and up-to-date exposition of the existing theory of viscosity solutions and regular solutions of second-order HJB equations in Hilbert spaces is given, together with an extensive survey of other methods, with a full bibliography. In particular, Chapter 6, written by M. Fuhrman and G. Tessitore, surveys the theory of regular solutions of HJB equations arising in infinite-dimensional stochastic control, via BSDEs. The book is of interest to both pure and applied researchers working in the control theory of stochastic PDEs, and in PDEs in infinite dimension. Readers from other fields who want to learn the basic theory will also find it useful. The prerequisites are: standard functional analysis, the theory of semigroups of operators and its use in the study of PDEs, some knowledge of the dynamic programming approach to stochastic optimal control problems in finite dimension, and the basics of stochastic analysis and stochastic equations in infinite-dimensional spaces.

Author : Altannar Chinchuluun,Panos M. Pardalos,Rentsen Enkhbat,Ider Tseveendorj
Publisher : Springer Science & Business Media
Page : 508 pages
File Size : 55,5 Mb
Release : 2010-08-05
Category : Mathematics
ISBN : 9780387894966

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Optimization and Optimal Control by Altannar Chinchuluun,Panos M. Pardalos,Rentsen Enkhbat,Ider Tseveendorj Pdf

Optimization and optimal control are the main tools in decision making. Because of their numerous applications in various disciplines, research in these areas is accelerating at a rapid pace. “Optimization and Optimal Control: Theory and Applications” brings together the latest developments in these areas of research as well as presents applications of these results to a wide range of real-world problems. This volume can serve as a useful resource for researchers, practitioners, and advanced graduate students of mathematics and engineering working in research areas where results in optimization and optimal control can be applied.

Author : Jiongmin Yong,Xun Yu Zhou
Publisher : Springer Science & Business Media
Page : 459 pages
File Size : 52,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461214663

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Stochastic Controls by Jiongmin Yong,Xun Yu Zhou Pdf

As is well known, Pontryagin's maximum principle and Bellman's dynamic programming are the two principal and most commonly used approaches in solving stochastic optimal control problems. * An interesting phenomenon one can observe from the literature is that these two approaches have been developed separately and independently. Since both methods are used to investigate the same problems, a natural question one will ask is the fol lowing: (Q) What is the relationship betwccn the maximum principlc and dy namic programming in stochastic optimal controls? There did exist some researches (prior to the 1980s) on the relationship between these two. Nevertheless, the results usually werestated in heuristic terms and proved under rather restrictive assumptions, which were not satisfied in most cases. In the statement of a Pontryagin-type maximum principle there is an adjoint equation, which is an ordinary differential equation (ODE) in the (finite-dimensional) deterministic case and a stochastic differential equation (SDE) in the stochastic case. The system consisting of the adjoint equa tion, the original state equation, and the maximum condition is referred to as an (extended) Hamiltonian system. On the other hand, in Bellman's dynamic programming, there is a partial differential equation (PDE), of first order in the (finite-dimensional) deterministic case and of second or der in the stochastic case. This is known as a Hamilton-Jacobi-Bellman (HJB) equation.