Stochastic Optimal Control of Structures

Stochastic Optimal Control of Structures PDF

Author: Yongbo Peng

Publisher: Springer

Published: 2019-06-27

Total Pages: 322

ISBN-13: 9811367647

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This book proposes, for the first time, a basic formulation for structural control that takes into account the stochastic dynamics induced by engineering excitations in the nature of non-stationary and non-Gaussian processes. Further, it establishes the theory of and methods for stochastic optimal control of randomly-excited engineering structures in the context of probability density evolution methods, such as physically-based stochastic optimal (PSO) control. By logically integrating randomness into control gain, the book helps readers design elegant control systems, mitigate risks in civil engineering structures, and avoid the dilemmas posed by the methods predominantly applied in current practice, such as deterministic control and classical linear quadratic Gaussian (LQG) control associated with nominal white noises.

Stochastic Optimal Control in Infinite Dimension

Stochastic Optimal Control in Infinite Dimension PDF

Author: Giorgio Fabbri

Publisher: Springer

Published: 2017-06-22

Total Pages: 916

ISBN-13: 3319530674

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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.

Deterministic and Stochastic Optimal Control

Deterministic and Stochastic Optimal Control PDF

Author: Wendell H. Fleming

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 231

ISBN-13: 1461263808

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This book may be regarded as consisting of two parts. In Chapters I-IV we pre sent what we regard as essential topics in an introduction to deterministic optimal control theory. This material has been used by the authors for one semester graduate-level courses at Brown University and the University of Kentucky. The simplest problem in calculus of variations is taken as the point of departure, in Chapter I. Chapters II, III, and IV deal with necessary conditions for an opti mum, existence and regularity theorems for optimal controls, and the method of dynamic programming. The beginning reader may find it useful first to learn the main results, corollaries, and examples. These tend to be found in the earlier parts of each chapter. We have deliberately postponed some difficult technical proofs to later parts of these chapters. In the second part of the book we give an introduction to stochastic optimal control for Markov diffusion processes. Our treatment follows the dynamic pro gramming method, and depends on the intimate relationship between second order partial differential equations of parabolic type and stochastic differential equations. This relationship is reviewed in Chapter V, which may be read inde pendently of Chapters I-IV. Chapter VI is based to a considerable extent on the authors' work in stochastic control since 1961. It also includes two other topics important for applications, namely, the solution to the stochastic linear regulator and the separation principle.

Optimal Stochastic Control Schemes within a Structural Reliability Framework

Optimal Stochastic Control Schemes within a Structural Reliability Framework PDF

Author: Bernt J. Leira

Publisher: Springer Science & Business Media

Published: 2013-09-07

Total Pages: 98

ISBN-13: 3319014056

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​The book addresses the topic of on-line implementation of structural and mechanical design criteria as an explicit part of optimal control schemes. The intention of the present research monograph is to reflect recent developments within this area. Examples of application of relevant control algorithms are included to illustrate their practical implementation. These examples are mainly taken from the area of marine technology with the multi-component external loading being represented as both varying in time and with magnitudes that are represented as statistical quantities. The relevant target group will be mechanical and structural engineers that are concerned with “smart components and structures” where optimal design principles and control actuators are combined. The book is also relevant for engineers e.g. involved in mechatronics and control applications.

Optimal Control and Estimation

Optimal Control and Estimation PDF

Author: Robert F. Stengel

Publisher: Courier Corporation

Published: 2012-10-16

Total Pages: 672

ISBN-13: 0486134814

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Graduate-level text provides introduction to optimal control theory for stochastic systems, emphasizing application of basic concepts to real problems.

Stochastic Multi-Stage Optimization

Stochastic Multi-Stage Optimization PDF

Author: Pierre Carpentier

Publisher: Springer

Published: 2015-05-05

Total Pages: 362

ISBN-13: 3319181386

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The focus of the present volume is stochastic optimization of dynamical systems in discrete time where - by concentrating on the role of information regarding optimization problems - it discusses the related discretization issues. There is a growing need to tackle uncertainty in applications of optimization. For example the massive introduction of renewable energies in power systems challenges traditional ways to manage them. This book lays out basic and advanced tools to handle and numerically solve such problems and thereby is building a bridge between Stochastic Programming and Stochastic Control. It is intended for graduates readers and scholars in optimization or stochastic control, as well as engineers with a background in applied mathematics.

Stochastic Dynamics of Structures

Stochastic Dynamics of Structures PDF

Author: Jie Li

Publisher: John Wiley & Sons

Published: 2009-07-23

Total Pages: 426

ISBN-13: 0470824255

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In Stochastic Dynamics of Structures, Li and Chen present a unified view of the theory and techniques for stochastic dynamics analysis, prediction of reliability, and system control of structures within the innovative theoretical framework of physical stochastic systems. The authors outline the fundamental concepts of random variables, stochastic process and random field, and orthogonal expansion of random functions. Readers will gain insight into core concepts such as stochastic process models for typical dynamic excitations of structures, stochastic finite element, and random vibration analysis. Li and Chen also cover advanced topics, including the theory of and elaborate numerical methods for probability density evolution analysis of stochastic dynamical systems, reliability-based design, and performance control of structures. Stochastic Dynamics of Structures presents techniques for researchers and graduate students in a wide variety of engineering fields: civil engineering, mechanical engineering, aerospace and aeronautics, marine and offshore engineering, ship engineering, and applied mechanics. Practicing engineers will benefit from the concise review of random vibration theory and the new methods introduced in the later chapters. "The book is a valuable contribution to the continuing development of the field of stochastic structural dynamics, including the recent discoveries and developments by the authors of the probability density evolution method (PDEM) and its applications to the assessment of the dynamic reliability and control of complex structures through the equivalent extreme-value distribution." —A. H-S. Ang, NAE, Hon. Mem. ASCE, Research Professor, University of California, Irvine, USA "The authors have made a concerted effort to present a responsible and even holistic account of modern stochastic dynamics. Beyond the traditional concepts, they also discuss theoretical tools of recent currency such as the Karhunen-Loeve expansion, evolutionary power spectra, etc. The theoretical developments are properly supplemented by examples from earthquake, wind, and ocean engineering. The book is integrated by also comprising several useful appendices, and an exhaustive list of references; it will be an indispensable tool for students, researchers, and practitioners endeavoring in its thematic field." —Pol Spanos, NAE, Ryon Chair in Engineering, Rice University, Houston, USA

Stochastic Optimal Control and the U.S. Financial Debt Crisis

Stochastic Optimal Control and the U.S. Financial Debt Crisis PDF

Author: Jerome L. Stein

Publisher: Springer Science & Business Media

Published: 2012-03-30

Total Pages: 167

ISBN-13: 1461430798

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Stochastic Optimal Control (SOC)—a mathematical theory concerned with minimizing a cost (or maximizing a payout) pertaining to a controlled dynamic process under uncertainty—has proven incredibly helpful to understanding and predicting debt crises and evaluating proposed financial regulation and risk management. Stochastic Optimal Control and the U.S. Financial Debt Crisis analyzes SOC in relation to the 2008 U.S. financial crisis, and offers a detailed framework depicting why such a methodology is best suited for reducing financial risk and addressing key regulatory issues. Topics discussed include the inadequacies of the current approaches underlying financial regulations, the use of SOC to explain debt crises and superiority over existing approaches to regulation, and the domestic and international applications of SOC to financial crises. Principles in this book will appeal to economists, mathematicians, and researchers interested in the U.S. financial debt crisis and optimal risk management.