Control Theory Of Systems Governed By Partial Differential Equations
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Control Theory Of Systems Governed By Partial Differential Equations
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Author : A.K. Aziz
language : en
Publisher: Academic Press
Release Date : 2014-05-10
Control Theory Of Systems Governed By Partial Differential Equations written by A.K. Aziz and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Technology & Engineering categories.
Control Theory of Systems Governed by Partial Differential Equations covers the proceedings of the 1976 Conference by the same title, held at the Naval Surface Weapons Center, Silver Spring, Maryland. The purpose of this conference is to examine the control theory of partial differential equations and its application. This text is divided into five chapters that primarily focus on tutorial lecture series on the theory of optimal control of distributed systems. It describes the many manifestations of the theory and its applications appearing in the other chapters. This work also presents the principles of the duality and asymptotic methods in control theory, including the variational principle for the heat equation. A chapter highlights systems that are not of the linear quadratic type. This chapter also explores the control of free surfaces and the geometrical control variables. The last chapter provides a summary of the features and applications of the numerical approximation of problems of optimal control. This book will prove useful to mathematicians, engineers, and researchers.
Optimal Control Of Systems Governed By Partial Differential Equations
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Author : Jacques Louis Lions
language : en
Publisher: Springer
Release Date : 1971-01-01
Optimal Control Of Systems Governed By Partial Differential Equations written by Jacques Louis Lions and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971-01-01 with Mathematics categories.
1. The development of a theory of optimal control (deterministic) requires the following initial data: (i) a control u belonging to some set ilIi ad (the set of 'admissible controls') which is at our disposition, (ii) for a given control u, the state y(u) of the system which is to be controlled is given by the solution of an equation (*) Ay(u)=given function ofu where A is an operator (assumed known) which specifies the system to be controlled (A is the 'model' of the system), (iii) the observation z(u) which is a function of y(u) (assumed to be known exactly; we consider only deterministic problems in this book), (iv) the "cost function" J(u) ("economic function") which is defined in terms of a numerical function z-+
Mathematical Control Of Coupled Pdes
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Author : Irena Lasiecka
language : en
Publisher: SIAM
Release Date : 2002-01-01
Mathematical Control Of Coupled Pdes written by Irena Lasiecka and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-01-01 with Mathematics categories.
Control Theory For Partial Differential Equations Volume 1 Abstract Parabolic Systems
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Author : Irena Lasiecka
language : en
Publisher: Cambridge University Press
Release Date : 2000-02-13
Control Theory For Partial Differential Equations Volume 1 Abstract Parabolic Systems written by Irena Lasiecka 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 2000-02-13 with Mathematics categories.
Originally published in 2000, this is the first volume of a comprehensive two-volume treatment of quadratic optimal control theory for partial differential equations over a finite or infinite time horizon, and related differential (integral) and algebraic Riccati equations. Both continuous theory and numerical approximation theory are included. The authors use an abstract space, operator theoretic approach, which is based on semigroups methods, and which is unifying across a few basic classes of evolution. The various abstract frameworks are motivated by, and ultimately directed to, partial differential equations with boundary/point control. Volume 1 includes the abstract parabolic theory for the finite and infinite cases and corresponding PDE illustrations as well as various abstract hyperbolic settings in the finite case. It presents numerous fascinating results. These volumes will appeal to graduate students and researchers in pure and applied mathematics and theoretical engineering with an interest in optimal control problems.
Optimal Control Of Systems Governed By Partial Differential Equations
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Author : Jacques-Louis Lions
language : en
Publisher: Springer
Release Date : 1971
Optimal Control Of Systems Governed By Partial Differential Equations written by Jacques-Louis Lions and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with Mathematics categories.
Control Theory Of Partial Differential Equations
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Author : Guenter Leugering
language : en
Publisher: CRC Press
Release Date : 2005-05-27
Control Theory Of Partial Differential Equations written by Guenter Leugering and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-05-27 with Mathematics categories.
The field of control theory in PDEs has broadened considerably as more realistic models have been introduced and investigated. This book presents a broad range of recent developments, new discoveries, and mathematical tools in the field. The authors discuss topics such as elasticity, thermo-elasticity, aero-elasticity, interactions between fluids a
Mathematical Control Theory For Stochastic Partial Differential Equations
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Author : Qi Lü
language : en
Publisher: Springer
Release Date : 2022-09-18
Mathematical Control Theory For Stochastic Partial Differential Equations written by Qi Lü and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-18 with Science categories.
This is the first book to systematically present control theory for stochastic distributed parameter systems, a comparatively new branch of mathematical control theory. The new phenomena and difficulties arising in the study of controllability and optimal control problems for this type of system are explained in detail. Interestingly enough, one has to develop new mathematical tools to solve some problems in this field, such as the global Carleman estimate for stochastic partial differential equations and the stochastic transposition method for backward stochastic evolution equations. In a certain sense, the stochastic distributed parameter control system is the most general control system in the context of classical physics. Accordingly, studying this field may also yield valuable insights into quantum control systems. A basic grasp of functional analysis, partial differential equations, and control theory for deterministic systems is the only prerequisite for reading this book.
Identification And Control In Systems Governed By Partial Differential Equations
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Author : H. Thomas Banks
language : en
Publisher: SIAM
Release Date : 1993-01-01
Identification And Control In Systems Governed By Partial Differential Equations written by H. Thomas Banks and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-01-01 with Science categories.
Real Time Pde Constrained Optimization
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Author : Lorenz T. Biegler
language : en
Publisher: SIAM
Release Date : 2007-07-12
Real Time Pde Constrained Optimization written by Lorenz T. Biegler and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-07-12 with Mathematics categories.
“…a timely contribution to a field of growing importance. This carefully edited book presents a rich collection of chapters ranging from mathematical methodology to emerging applications. I recommend it to students as a rigorous and comprehensive presentation of simulation-based optimization and to researchers as an overview of recent advances and challenges in the field.” — Jorge Nocedal, Professor, Northwestern University.Many engineering and scientific problems in design, control, and parameter estimation can be formulated as optimization problems that are governed by partial differential equations (PDEs). The complexities of the PDEs—and the requirement for rapid solution—pose significant difficulties. A particularly challenging class of PDE-constrained optimization problems is characterized by the need for real-time solution, i.e., in time scales that are sufficiently rapid to support simulation-based decision making. Real-Time PDE-Constrained Optimization, the first book devoted to real-time optimization for systems governed by PDEs, focuses on new formulations, methods, and algorithms needed to facilitate real-time, PDE-constrained optimization. In addition to presenting state-of-the-art algorithms and formulations, the text illustrates these algorithms with a diverse set of applications that includes problems in the areas of aerodynamics, biology, fluid dynamics, medicine, chemical processes, homeland security, and structural dynamics. Despite difficulties, there is a pressing need to capitalize on continuing advances in computing power to develop optimization methods that will replace simple rule-based decision making with optimized decisions based on complex PDE simulations. Audience The book is aimed at readers who have expertise in simulation and are interested in incorporating optimization into their simulations, who have expertise in numerical optimization and are interested in adapting optimization methods to the class of infinite-dimensional simulation problems, or who have worked in “offline” optimization contexts and are interested in moving to “online” optimization.Contents Preface; Part I: Concepts and Properties of Real-Time, Online Strategies. Chapter 1: Constrained Optimal Feedback Control of Systems Governed by Large Differential Algebraic Equations; Chapter 2: A Stabilizing Real-Time Implementation of Nonlinear Model Predictive Control; Chapter 3: Numerical Feedback Controller Design for PDE Systems Using Model Reduction: Techniques and Case Studies; Chapter 4: Least-Squares Finite Element Method for Optimization and Control Problems; Part II: Fast PDE-Constrained Optimization Solvers. Chapter 5: Space-Time Multigrid Methods for Solving Unsteady Optimal Control Problems; Chapter 6: A Time-Parallel Implicit Methodology for the Near-Real-Time Solution of Systems of Linear Oscillators; Chapter 7: Generalized SQP Methods with “Parareal” Time-Domain Decomposition for Time-Dependent PDE-Constrained Optimization; Chapter 8: Simultaneous Pseudo-Timestepping for State-Constrained Optimization Problems in Aerodynamics; Chapter 9: Digital Filter Stepsize Control in DASPK and Its Effect on Control Optimization Performance; Part III: Reduced Order Modeling. Chapter 10: Certified Rapid Solution of Partial Differential Equations for Real-Time Parameter Estimation and Optimization; Chapter 11: Model Reduction for Large-Scale Applications in Computational Fluid Dynamics; Chapter 12: Suboptimal Feedback Control of Flow Separation by POD Model Reduction; Part IV: Applications. Chapter 13: A Combined Shape-Newton and Topology Optimization Technique in Real-Time Image Segmentation; Chapter 14: COFIR: Coarse and Fine Image Registration; Chapter 15: Real-Time, Large Scale Optimization of Water Network Systems Using a Sub-domain Approach; Index.
Optimal Control Of Partial Differential Equations
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Author : Fredi Tröltzsch
language : en
Publisher: American Mathematical Soc.
Release Date : 2010
Optimal Control Of Partial Differential Equations written by Fredi Tröltzsch and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
Optimal control theory is concerned with finding control functions that minimize cost functions for systems described by differential equations. This book focuses on optimal control problems where the state equation is an elliptic or parabolic partial differential equation. It includes topics on the existence of optimal solutions.