Numerical Methods For Optimal Control Problems

Author : Maurizio Falcone,Roberto Ferretti,Lars Grüne,William M. McEneaney
Publisher : Springer
Page : 0 pages
File Size : 52,8 Mb
Release : 2019-02-05
Category : Science
ISBN : 3030019586

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Numerical Methods for Optimal Control Problems by Maurizio Falcone,Roberto Ferretti,Lars Grüne,William M. McEneaney Pdf

This work presents recent mathematical methods in the area of optimal control with a particular emphasis on the computational aspects and applications. Optimal control theory concerns the determination of control strategies for complex dynamical systems, in order to optimize some measure of their performance. Started in the 60's under the pressure of the "space race" between the US and the former USSR, the field now has a far wider scope, and embraces a variety of areas ranging from process control to traffic flow optimization, renewable resources exploitation and management of financial markets. These emerging applications require more and more efficient numerical methods for their solution, a very difficult task due the huge number of variables. The chapters of this volume give an up-to-date presentation of several recent methods in this area including fast dynamic programming algorithms, model predictive control and max-plus techniques. This book is addressed to researchers, graduate students and applied scientists working in the area of control problems, differential games and their applications.

Author : Radoslaw Pytlak
Publisher : Springer Science & Business Media
Page : 244 pages
File Size : 41,8 Mb
Release : 1999-08-19
Category : Science
ISBN : 3540662146

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Numerical Methods for Optimal Control Problems with State Constraints by Radoslaw Pytlak Pdf

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 : Harold Kushner,Paul G. Dupuis
Publisher : Springer Science & Business Media
Page : 480 pages
File Size : 50,6 Mb
Release : 2013-11-27
Category : Mathematics
ISBN : 9781461300076

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Numerical Methods for Stochastic Control Problems in Continuous Time by Harold Kushner,Paul G. Dupuis Pdf

Stochastic control is a very active area of research. This monograph, written by two leading authorities in the field, has been updated to reflect the latest developments. It covers effective numerical methods for stochastic control problems in continuous time on two levels, that of practice and that of mathematical development. It is broadly accessible for graduate students and researchers.

Author : Radoslaw Pytlak
Publisher : Springer
Page : 224 pages
File Size : 45,6 Mb
Release : 2006-11-14
Category : Science
ISBN : 9783540486626

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Numerical Methods for Optimal Control Problems with State Constraints by Radoslaw Pytlak Pdf

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 : Alfio Borzi,Gabriele Ciaramella,Martin Sprengel
Publisher : SIAM
Page : 396 pages
File Size : 44,8 Mb
Release : 2017-07-06
Category : Technology & Engineering
ISBN : 9781611974836

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Formulation and Numerical Solution of Quantum Control Problems by Alfio Borzi,Gabriele Ciaramella,Martin Sprengel Pdf

This book provides an introduction to representative nonrelativistic quantum control problems and their theoretical analysis and solution via modern computational techniques. The quantum theory framework is based on the Schr?dinger picture, and the optimization theory, which focuses on functional spaces, is based on the Lagrange formalism. The computational techniques represent recent developments that have resulted from combining modern numerical techniques for quantum evolutionary equations with sophisticated optimization schemes. Both finite and infinite-dimensional models are discussed, including the three-level Lambda system arising in quantum optics, multispin systems in NMR, a charged particle in a well potential, Bose?Einstein condensates, multiparticle spin systems, and multiparticle models in the time-dependent density functional framework. This self-contained book covers the formulation, analysis, and numerical solution of quantum control problems and bridges scientific computing, optimal control and exact controllability, optimization with differential models, and the sciences and engineering that require quantum control methods. ??

Author : Maurizio Falcone,Roberto Ferretti,Lars Grüne,William M. McEneaney
Publisher : Springer
Page : 275 pages
File Size : 45,5 Mb
Release : 2019-01-26
Category : Science
ISBN : 9783030019594

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Numerical Methods for Optimal Control Problems by Maurizio Falcone,Roberto Ferretti,Lars Grüne,William M. McEneaney Pdf

This work presents recent mathematical methods in the area of optimal control with a particular emphasis on the computational aspects and applications. Optimal control theory concerns the determination of control strategies for complex dynamical systems, in order to optimize some measure of their performance. Started in the 60's under the pressure of the "space race" between the US and the former USSR, the field now has a far wider scope, and embraces a variety of areas ranging from process control to traffic flow optimization, renewable resources exploitation and management of financial markets. These emerging applications require more and more efficient numerical methods for their solution, a very difficult task due the huge number of variables. The chapters of this volume give an up-to-date presentation of several recent methods in this area including fast dynamic programming algorithms, model predictive control and max-plus techniques. This book is addressed to researchers, graduate students and applied scientists working in the area of control problems, differential games and their applications.

Author : Bulirsch,Miele,Stoer,Well
Publisher : Birkhäuser
Page : 352 pages
File Size : 49,9 Mb
Release : 2013-03-08
Category : Science
ISBN : 9783034875394

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Optimal Control by Bulirsch,Miele,Stoer,Well Pdf

"Optimal Control" reports on new theoretical and practical advances essential for analysing and synthesizing optimal controls of dynamical systems governed by partial and ordinary differential equations. New necessary and sufficient conditions for optimality are given. Recent advances in numerical methods are discussed. These have been achieved through new techniques for solving large-sized nonlinear programs with sparse Hessians, and through a combination of direct and indirect methods for solving the multipoint boundary value problem. The book also focuses on the construction of feedback controls for nonlinear systems and highlights advances in the theory of problems with uncertainty. Decomposition methods of nonlinear systems and new techniques for constructing feedback controls for state- and control constrained linear quadratic systems are presented. The book offers solutions to many complex practical optimal control problems.

Author : John T. Betts
Publisher : SIAM
Page : 442 pages
File Size : 44,8 Mb
Release : 2010-01-01
Category : Mathematics
ISBN : 9780898716887

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Practical Methods for Optimal Control and Estimation Using Nonlinear Programming by John T. Betts Pdf

A focused presentation of how sparse optimization methods can be used to solve optimal control and estimation problems.

Author : J Gregory
Publisher : CRC Press
Page : 242 pages
File Size : 42,6 Mb
Release : 2018-01-18
Category : Mathematics
ISBN : 9781351087766

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Constrained Optimization In The Calculus Of Variations and Optimal Control Theory by J Gregory Pdf

The major purpose of this book is to present the theoretical ideas and the analytical and numerical methods to enable the reader to understand and efficiently solve these important optimizational problems.The first half of this book should serve as the major component of a classical one or two semester course in the calculus of variations and optimal control theory. The second half of the book will describe the current research of the authors which is directed to solving these problems numerically. In particular, we present new reformulations of constrained problems which leads to unconstrained problems in the calculus of variations and new general, accurate and efficient numerical methods to solve the reformulated problems. We believe that these new methods will allow the reader to solve important problems.

Author : Anonim
Publisher : Elsevier
Page : 596 pages
File Size : 43,5 Mb
Release : 2022-02-15
Category : Mathematics
ISBN : 9780323853392

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Numerical Control: Part A by Anonim Pdf

Numerical Control: Part A, Volume 23 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 Numerics for finite-dimensional control systems, Moments and convex optimization for analysis and control of nonlinear PDEs, The turnpike property in optimal control, Structure-Preserving Numerical Schemes for Hamiltonian Dynamics, Optimal Control of PDEs and FE-Approximation, Filtration techniques for the uniform controllability of semi-discrete hyperbolic equations, Numerical controllability properties of fractional partial differential equations, Optimal Control, Numerics, and Applications of Fractional PDEs, 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 : Harold Kushner,Paul G. Dupuis
Publisher : Springer Science & Business Media
Page : 436 pages
File Size : 47,7 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781468404418

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Numerical Methods for Stochastic Control Problems in Continuous Time by Harold Kushner,Paul G. Dupuis Pdf

This book is concerned with numerical methods for stochastic control and optimal stochastic control problems. The random process models of the controlled or uncontrolled stochastic systems are either diffusions or jump diffusions. Stochastic control is a very active area of research and new prob lem formulations and sometimes surprising applications appear regularly. We have chosen forms of the models which cover the great bulk of the for mulations of the continuous time stochastic control problems which have appeared to date. The standard formats are covered, but much emphasis is given to the newer and less well known formulations. The controlled process might be either stopped or absorbed on leaving a constraint set or upon first hitting a target set, or it might be reflected or "projected" from the boundary of a constraining set. In some of the more recent applications of the reflecting boundary problem, for example the so-called heavy traffic approximation problems, the directions of reflection are actually discontin uous. In general, the control might be representable as a bounded function or it might be of the so-called impulsive or singular control types. Both the "drift" and the "variance" might be controlled. The cost functions might be any of the standard types: Discounted, stopped on first exit from a set, finite time, optimal stopping, average cost per unit time over the infinite time interval, and so forth.

Author : Sebastian Sager
Publisher : Unknown
Page : 219 pages
File Size : 47,6 Mb
Release : 2005
Category : Optimale Kontrolle - Gemischt-ganzzahlige Optimierung - Mehrzielmethode
ISBN : 3899594169

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Numerical Methods for Mixed-integer Optimal Control Problems by Sebastian Sager Pdf

Author : Bulirsch,Miele,Stoer,Well
Publisher : Birkhäuser
Page : 350 pages
File Size : 47,6 Mb
Release : 1993-08-30
Category : Science
ISBN : 3764328878

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Optimal Control by Bulirsch,Miele,Stoer,Well Pdf

"Optimal Control" reports on new theoretical and practical advances essential for analysing and synthesizing optimal controls of dynamical systems governed by partial and ordinary differential equations. New necessary and sufficient conditions for optimality are given. Recent advances in numerical methods are discussed. These have been achieved through new techniques for solving large-sized nonlinear programs with sparse Hessians, and through a combination of direct and indirect methods for solving the multipoint boundary value problem. The book also focuses on the construction of feedback controls for nonlinear systems and highlights advances in the theory of problems with uncertainty. Decomposition methods of nonlinear systems and new techniques for constructing feedback controls for state- and control constrained linear quadratic systems are presented. The book offers solutions to many complex practical optimal control problems.

Author : Peter Falb
Publisher : Springer Nature
Page : 311 pages
File Size : 50,5 Mb
Release : 2020-01-02
Category : Science
ISBN : 9780817647230

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Direct Methods in Control Problems by Peter Falb Pdf

Various general techniques have been developed for control and systems problems, many of which involve indirect methods. Because these indirect methods are not always effective, alternative approaches using direct methods are of particular interest and relevance given the advances of computing in recent years. The focus of this book, unique in the literature, is on direct methods, which are concerned with finding actual solutions to problems in control and systems, often algorithmic in nature. Throughout the work, deterministic and stochastic problems are examined from a unified perspective and with considerable rigor. Emphasis is placed on the theoretical basis of the methods and their potential utility in a broad range of control and systems problems. The book is an excellent reference for graduate students, researchers, applied mathematicians, and control engineers and may be used as a textbook for a graduate course or seminar on direct methods in control.

Author : Simant Ranjan Upreti
Publisher : CRC Press
Page : 305 pages
File Size : 44,7 Mb
Release : 2016-04-19
Category : Science
ISBN : 9781439838952

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Optimal Control for Chemical Engineers by Simant Ranjan Upreti Pdf

This self-contained book gives a detailed treatment of optimal control theory that enables readers to formulate and solve optimal control problems. With a strong emphasis on problem solving, it provides all the necessary mathematical analyses and derivations of important results, including multiplier theorems and Pontryagin's principle. The text presents various examples and basic concepts of optimal control and describes important numerical methods and computational algorithms for solving a wide range of optimal control problems, including periodic processes.