Stochastic Control Of Partially Observable Systems
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Stochastic Control Of Partially Observable Systems
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Author : Alain Bensoussan
language : en
Publisher: Cambridge University Press
Release Date : 1992-08-13
Stochastic Control Of Partially Observable Systems written by Alain Bensoussan and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-08-13 with Mathematics categories.
These systems play an important role in many applications.
Stochastic Control Theory
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Author : Makiko Nisio
language : en
Publisher: Springer
Release Date : 2014-11-27
Stochastic Control Theory written by Makiko Nisio and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-27 with Mathematics categories.
This book offers a systematic introduction to the optimal stochastic control theory via the dynamic programming principle, which is a powerful tool to analyze control problems. First we consider completely observable control problems with finite horizons. Using a time discretization we construct a nonlinear semigroup related to the dynamic programming principle (DPP), whose generator provides the Hamilton–Jacobi–Bellman (HJB) equation, and we characterize the value function via the nonlinear semigroup, besides the viscosity solution theory. When we control not only the dynamics of a system but also the terminal time of its evolution, control-stopping problems arise. This problem is treated in the same frameworks, via the nonlinear semigroup. Its results are applicable to the American option price problem. Zero-sum two-player time-homogeneous stochastic differential games and viscosity solutions of the Isaacs equations arising from such games are studied via a nonlinear semigroup related to DPP (the min-max principle, to be precise). Using semi-discretization arguments, we construct the nonlinear semigroups whose generators provide lower and upper Isaacs equations. Concerning partially observable control problems, we refer to stochastic parabolic equations driven by colored Wiener noises, in particular, the Zakai equation. The existence and uniqueness of solutions and regularities as well as Itô's formula are stated. A control problem for the Zakai equations has a nonlinear semigroup whose generator provides the HJB equation on a Banach space. The value function turns out to be a unique viscosity solution for the HJB equation under mild conditions. This edition provides a more generalized treatment of the topic than does the earlier book Lectures on Stochastic Control Theory (ISI Lecture Notes 9), where time-homogeneous cases are dealt with. Here, for finite time-horizon control problems, DPP was formulated as a one-parameter nonlinear semigroup, whose generator provides the HJB equation, by using a time-discretization method. The semigroup corresponds to the value function and is characterized as the envelope of Markovian transition semigroups of responses for constant control processes. Besides finite time-horizon controls, the book discusses control-stopping problems in the same frameworks.
Stochastic Controls
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Author : Jiongmin Yong
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Stochastic Controls written by Jiongmin Yong and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Advances In Statistical Control Algebraic Systems Theory And Dynamic Systems Characteristics
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Author : Chang-Hee Won
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-07-08
Advances In Statistical Control Algebraic Systems Theory And Dynamic Systems Characteristics written by Chang-Hee Won and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-07-08 with Mathematics categories.
This volume is a collection of chapters covering recent advances in stochastic optimal control theory and algebraic systems theory. The book will be a useful reference for researchers and graduate students in systems and control, algebraic systems theory, and applied mathematics. Requiring only knowledge of undergraduate-level control and systems theory, the work may be used as a supplementary textbook in a graduate course on optimal control or algebraic systems theory.
An Introduction To Optimal Control Of Fbsde With Incomplete Information
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Author : Guangchen Wang
language : en
Publisher: Springer
Release Date : 2018-05-16
An Introduction To Optimal Control Of Fbsde With Incomplete Information written by Guangchen Wang and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-16 with Mathematics categories.
This book focuses on maximum principle and verification theorem for incomplete information forward-backward stochastic differential equations (FBSDEs) and their applications in linear-quadratic optimal controls and mathematical finance. Lots of interesting phenomena arising from the area of mathematical finance can be described by FBSDEs. Optimal control problems of FBSDEs are theoretically important and practically relevant. A standard assumption in the literature is that the stochastic noises in the model are completely observed. However, this is rarely the case in real world situations. The optimal control problems under complete information are studied extensively. Nevertheless, very little is known about these problems when the information is not complete. The aim of this book is to fill this gap. This book is written in a style suitable for graduate students and researchers in mathematics and engineering with basic knowledge of stochastic process, optimal control and mathematical finance.
Partially Observable Linear Systems Under Dependent Noises
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Author : Agamirza E. Bashirov
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Partially Observable Linear Systems Under Dependent Noises written by Agamirza E. Bashirov and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
Noise is a rich concept playing an underlying role in human activity. Consideration of the noise phenomenon in arts and sciences, respectively, makes the distinction between both domains more obvious. Artists create "deliberate noise"`; the masterpieces of literature, music, modern fine art etc. are those where a clear idea, traditionally related to such concepts as love, is presented under a skilful veil of "deliberate noise". On the contrary, sciences fight against noise; a scientific discovery is a law of nature extracted from a noisy medium and refined. This book discusses the methods of fighting against noise. It can be regarded as a mathematical view of specific engineering problems with known and new methods of control and estimation in noisy media. The main feature of this book is the investigation of stochastic optimal control and estimation problems with the noise processes acting dependently on the state (or signal) and observation systems. While multiple early and recent findings on the subject have been obtained and challenging problems remain to be solved, this subject has not yet been dealt with systematically nor properly investigated. The discussion is given for infinite dimensional systems, but within the linear quadratic framework for continuous and finite time horizon. In order to make this book self-contained, some background material is provided. Consequently, the target readers of this book are both applied mathematicians and theoretically oriented engineers who are designing new technology, as well as students of the related branches. The book may also be used as a reference manual in that part of functional analysis that is needed for problems of infinite dimensional linear systems theory.
Stochastics In Finite And Infinite Dimensions
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Author : Takeyuki Hida
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Stochastics In Finite And Infinite Dimensions written by Takeyuki Hida and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
During the last fifty years, Gopinath Kallianpur has made extensive and significant contributions to diverse areas of probability and statistics, including stochastic finance, Fisher consistent estimation, non-linear prediction and filtering problems, zero-one laws for Gaussian processes and reproducing kernel Hilbert space theory, and stochastic differential equations in infinite dimensions. To honor Kallianpur's pioneering work and scholarly achievements, a number of leading experts have written research articles highlighting progress and new directions of research in these and related areas. This commemorative volume, dedicated to Kallianpur on the occasion of his seventy-fifth birthday, will pay tribute to his multi-faceted achievements and to the deep insight and inspiration he has so graciously offered his students and colleagues throughout his career. Contributors to the volume: S. Aida, N. Asai, K. B. Athreya, R. N. Bhattacharya, A. Budhiraja, P. S. Chakraborty, P. Del Moral, R. Elliott, L. Gawarecki, D. Goswami, Y. Hu, J. Jacod, G. W. Johnson, L. Johnson, T. Koski, N. V. Krylov, I. Kubo, H.-H. Kuo, T. G. Kurtz, H. J. Kushner, V. Mandrekar, B. Margolius, R. Mikulevicius, I. Mitoma, H. Nagai, Y. Ogura, K. R. Parthasarathy, V. Perez-Abreu, E. Platen, B. V. Rao, B. Rozovskii, I. Shigekawa, K. B. Sinha, P. Sundar, M. Tomisaki, M. Tsuchiya, C. Tudor, W. A. Woycynski, J. Xiong.
Partially Observed Markov Decision Processes
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Author : Vikram Krishnamurthy
language : en
Publisher: Cambridge University Press
Release Date : 2016-03-21
Partially Observed Markov Decision Processes written by Vikram Krishnamurthy and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-21 with Technology & Engineering categories.
Covering formulation, algorithms, and structural results, and linking theory to real-world applications in controlled sensing (including social learning, adaptive radars and sequential detection), this book focuses on the conceptual foundations of partially observed Markov decision processes (POMDPs). It emphasizes structural results in stochastic dynamic programming, enabling graduate students and researchers in engineering, operations research, and economics to understand the underlying unifying themes without getting weighed down by mathematical technicalities. Bringing together research from across the literature, the book provides an introduction to nonlinear filtering followed by a systematic development of stochastic dynamic programming, lattice programming and reinforcement learning for POMDPs. Questions addressed in the book include: when does a POMDP have a threshold optimal policy? When are myopic policies optimal? How do local and global decision makers interact in adaptive decision making in multi-agent social learning where there is herding and data incest? And how can sophisticated radars and sensors adapt their sensing in real time?
Robust Control Design Using H Methods
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Author : Ian R. Petersen
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Robust Control Design Using H Methods written by Ian R. Petersen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Technology & Engineering categories.
This is a unified collection of important recent results for the design of robust controllers for uncertain systems, primarily based on H8 control theory or its stochastic counterpart, risk sensitive control theory. Two practical applications are used to illustrate the methods throughout.
Advances In Stochastic Structural Dynamics
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Author : W. Q. Zhu
language : en
Publisher: CRC Press
Release Date : 2003-05-13
Advances In Stochastic Structural Dynamics written by W. Q. Zhu and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-05-13 with Technology & Engineering categories.
Collection of technical papers presented at the 5th International Conference on Stochastic Structural Dynamics (SSD03) in Hangzhou, China during May 26-28, 2003. Topics include direct transfer substructure method for random response analysis, generation of bounded stochastic processes, and sample path behavior of Gaussian processes.