An ADMM Approach to the Numerical Solution of State Constrained Optimal Control Problems for Systems Modeled by Linear Parabolic Equations PDF Download

Author: Yongcun Song
Publisher:
ISBN:
Category : Electronic books
Languages : en
Pages : 56

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Book Description

Author: Emmanuel Trélat
Publisher: Elsevier
ISBN: 0323858260
Category : Mathematics
Languages : en
Pages : 662

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Book Description
Numerical Control: Part B, Volume 24 in the Handbook of Numerical Analysis series, highlights new advances in the field, with this new volume presenting interesting chapters written by an international board of authors. Chapters in this volume include Control problems in the coefficients and the domain for linear elliptic equations, Computational approaches for extremal geometric eigenvalue problems, Non-overlapping domain decomposition in space and time for PDE-constrained optimal control problems on networks, Feedback Control of Time-dependent Nonlinear PDEs with Applications in Fluid Dynamics, Stabilization of the Navier-Stokes equations - Theoretical and numerical aspects, Reconstruction algorithms based on Carleman estimates, and more. Other sections cover Discrete time formulations as time discretization strategies in data assimilation, Back and forth iterations/Time reversal methods, Unbalanced Optimal Transport: from Theory to Numerics, An ADMM Approach to the Exact and Approximate Controllability of Parabolic Equations, Nonlocal balance laws -- an overview over recent results, Numerics and control of conservation laws, Numerical approaches for simulation and control of superconducting quantum circuits, and much more. - Provides the authority and expertise of leading contributors from an international board of authors - Presents the latest release in the Handbook of Numerical Analysis series - Updated release includes the latest information on Numerical Control

Author: Radoslaw Pytlak
Publisher: Springer
ISBN: 3540486623
Category : Science
Languages : en
Pages : 224

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Book Description
While optimality conditions for optimal control problems with state constraints have been extensively investigated in the literature the results pertaining to numerical methods are relatively scarce. This book fills the gap by providing a family of new methods. Among others, a novel convergence analysis of optimal control algorithms is introduced. The analysis refers to the topology of relaxed controls only to a limited degree and makes little use of Lagrange multipliers corresponding to state constraints. This approach enables the author to provide global convergence analysis of first order and superlinearly convergent second order methods. Further, the implementation aspects of the methods developed in the book are presented and discussed. The results concerning ordinary differential equations are then extended to control problems described by differential-algebraic equations in a comprehensive way for the first time in the literature.

Author: Talaat Abdelhamid
Publisher: LAP Lambert Academic Publishing
ISBN: 9783848430482
Category :
Languages : en
Pages : 80

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Book Description
The optimal control problems governed by partial differential equations have developed very fast in the last 30 years, and it has brought a promising and vital researching domain to the subject of mathematics. The optimal control problems governed by partial differential equations concern many applications in physics, chemistry, biology, etc., such as materials design, crystal growth, temperature control, petroleum exploitation, and so on. The partial differential equations involved in these problems include elliptic equations, parabolic equations and hyperbolic equations. Our objective of this book, which consists of three chapters, aims to introduce the analytical and numerical solutions of constrained optimal control problems of quasilinear parabolic systems.

Author: Lorenz T. Biegler
Publisher: SIAM
ISBN: 9781611972252
Category : Control theory
Languages : en
Pages : 355

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Book Description
Differential-algebraic equations are the most natural way to mathematically model many complex systems in science and engineering. Once the model is derived, it is important to optimize the design parameters and control it in the most robust and efficient way to maximize performance. This book presents the latest theory and numerical methods for the optimal control of differential-algebraic equations. The following features are presented in a readable fashion so the results are accessible to the widest audience: the most recent theory, written by leading experts from a number of academic and nonacademic areas and departments; several state-of-the-art numerical methods; and real-world applications.

Author: Hee-Dae Kwon
Publisher:
ISBN:
Category :
Languages : en
Pages : 122

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Book Description
Terminal-state tracking optimal control problems for linear and semilinear parabolic equations are studied. The control objective is to track a desired terminal state and the control is of the distributed type. A distinctive feature of this work is that the controlled state and the target state are allowed to have nonmatching boundary conditions. In the linear case, analytic solution formulae for the optimal control problems are derived in the form of eigen series. Pointwise-in-time L2 norm estimates for the optimal solutions are obtained and approximate controllability results are established. Exact controllability is shown when the target state and the controlled state have matching boundary conditions. One-dimensional computational results are presented which illustrate the terminal-state tracking properties for the solutions expressed by the series formulae. In the semilinear case, the existence of an optimal control solution is shown. The dynamics of the optimal control solution is analyzed. Error estimates are obtained for semidiscrete (spatially discrete) approximations of the optimal control problem in tow and three space dimensions. A gradient algorithm is discussed and numerical results are presented.

Author: Kees C. P. Machielsen
Publisher:
ISBN:
Category : Boundary value problems
Languages : en
Pages : 232

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Book Description

Author: Volker L. Mehrmann
Publisher: Lecture Notes in Control and Information Sciences
ISBN:
Category : Language Arts & Disciplines
Languages : en
Pages : 192

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Book Description
A survey is given on the state of the art in theory and numerical solution of general autonomous linear quadratic optimal control problems (continuous and discrete) with differential algebraic equation constraints. It incorporates the newest developments on differential algebraic equations, Riccati equations and invariant subspace problems. In particular, it gives a decision chart of numerical methods, that can be used to determine the right numerical method according to special properties of the problem. The book closes a gap between mathematical theory, numerical solution and engineering application. The mathematical tools are kept as basic as possible in order to address the different groups of readers, mathematicians and engineers.

Author: Dan Tiba
Publisher: Springer
ISBN: 3540467556
Category : Science
Languages : en
Pages : 166

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Book Description
The book is devoted to the study of distributed control problems governed by various nonsmooth state systems. The main questions investigated include: existence of optimal pairs, first order optimality conditions, state-constrained systems, approximation and discretization, bang-bang and regularity properties for optimal control. In order to give the reader a better overview of the domain, several sections deal with topics that do not enter directly into the announced subject: boundary control, delay differential equations. In a subject still actively developing, the methods can be more important than the results and these include: adapted penalization techniques, the singular control systems approach, the variational inequality method, the Ekeland variational principle. Some prerequisites relating to convex analysis, nonlinear operators and partial differential equations are collected in the first chapter or are supplied appropriately in the text. The monograph is intended for graduate students and for researchers interested in this area of mathematics.

Author:
Publisher: Elsevier
ISBN: 0080956262
Category : Mathematics
Languages : en
Pages : 204

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Book Description
In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; andmethods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory.As a result, the book represents a blend of new methods in general computational analysis,and specific, but also generic, techniques for study of systems theory ant its particularbranches, such as optimal filtering and information compression.- Best operator approximation,- Non-Lagrange interpolation,- Generic Karhunen-Loeve transform- Generalised low-rank matrix approximation- Optimal data compression- Optimal nonlinear filtering