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Author: Stephen J. Kahne Publisher: ISBN: Category : Control theory Languages : en Pages : 30
Book Description
The application of Bellman's dynamic programming technique to realistic control problems has generally been precluded by excessive storage requirements inherent in the method. In this paper, the notion of state mobility is described and shown to be valuable in reducing certain classes of dynamic programming calculations to manageable size. The scheme requires one simple calculation at each stage of the process. IN many cases even this calculation may be omitted. It results in the reduction of the range of allowable state variables to be scanned. The amount of reduction varies from problem to problem. A simple example exhibits a fifty percent reduction. This corresponds to a fifty percent reduction in storage requirements for the problem. Reductions of one or two orders of magnitude appear possible for certain classes of problems.
Author: Stephen J. Kahne Publisher: ISBN: Category : Control theory Languages : en Pages : 30
Book Description
The application of Bellman's dynamic programming technique to realistic control problems has generally been precluded by excessive storage requirements inherent in the method. In this paper, the notion of state mobility is described and shown to be valuable in reducing certain classes of dynamic programming calculations to manageable size. The scheme requires one simple calculation at each stage of the process. IN many cases even this calculation may be omitted. It results in the reduction of the range of allowable state variables to be scanned. The amount of reduction varies from problem to problem. A simple example exhibits a fifty percent reduction. This corresponds to a fifty percent reduction in storage requirements for the problem. Reductions of one or two orders of magnitude appear possible for certain classes of problems.
Author: Stephen J. Kahne Publisher: ISBN: Category : Control theory Languages : en Pages : 0
Book Description
The application of Bellman's dynamic programming technique to realistic control problems has generally been precluded by excessive storage requirements inherent in the method. In this paper, the notion of state mobility is described and shown to be valuable in reducing certain classes of dynamic programming calculations to manageable size. The scheme requires one simple calculation at each stage of the process. IN many cases even this calculation may be omitted. It results in the reduction of the range of allowable state variables to be scanned. The amount of reduction varies from problem to problem. A simple example exhibits a fifty percent reduction. This corresponds to a fifty percent reduction in storage requirements for the problem. Reductions of one or two orders of magnitude appear possible for certain classes of problems.
Author: Dimitri Bertsekas Publisher: Athena Scientific ISBN: 1886529442 Category : Mathematics Languages : en Pages : 715
Book Description
This is the leading and most up-to-date textbook on the far-ranging algorithmic methodology of Dynamic Programming, which can be used for optimal control, Markovian decision problems, planning and sequential decision making under uncertainty, and discrete/combinatorial optimization. The treatment focuses on basic unifying themes, and conceptual foundations. It illustrates the versatility, power, and generality of the method with many examples and applications from engineering, operations research, and other fields. It also addresses extensively the practical application of the methodology, possibly through the use of approximations, and provides an extensive treatment of the far-reaching methodology of Neuro-Dynamic Programming/Reinforcement Learning. Among its special features, the book 1) provides a unifying framework for sequential decision making, 2) treats simultaneously deterministic and stochastic control problems popular in modern control theory and Markovian decision popular in operations research, 3) develops the theory of deterministic optimal control problems including the Pontryagin Minimum Principle, 4) introduces recent suboptimal control and simulation-based approximation techniques (neuro-dynamic programming), which allow the practical application of dynamic programming to complex problems that involve the dual curse of large dimension and lack of an accurate mathematical model, 5) provides a comprehensive treatment of infinite horizon problems in the second volume, and an introductory treatment in the first volume.
Author: Huaguang Zhang Publisher: Springer Science & Business Media ISBN: 144714757X Category : Technology & Engineering Languages : en Pages : 432
Book Description
There are many methods of stable controller design for nonlinear systems. In seeking to go beyond the minimum requirement of stability, Adaptive Dynamic Programming in Discrete Time approaches the challenging topic of optimal control for nonlinear systems using the tools of adaptive dynamic programming (ADP). The range of systems treated is extensive; affine, switched, singularly perturbed and time-delay nonlinear systems are discussed as are the uses of neural networks and techniques of value and policy iteration. The text features three main aspects of ADP in which the methods proposed for stabilization and for tracking and games benefit from the incorporation of optimal control methods: • infinite-horizon control for which the difficulty of solving partial differential Hamilton–Jacobi–Bellman equations directly is overcome, and proof provided that the iterative value function updating sequence converges to the infimum of all the value functions obtained by admissible control law sequences; • finite-horizon control, implemented in discrete-time nonlinear systems showing the reader how to obtain suboptimal control solutions within a fixed number of control steps and with results more easily applied in real systems than those usually gained from infinite-horizon control; • nonlinear games for which a pair of mixed optimal policies are derived for solving games both when the saddle point does not exist, and, when it does, avoiding the existence conditions of the saddle point. Non-zero-sum games are studied in the context of a single network scheme in which policies are obtained guaranteeing system stability and minimizing the individual performance function yielding a Nash equilibrium. In order to make the coverage suitable for the student as well as for the expert reader, Adaptive Dynamic Programming in Discrete Time: • establishes the fundamental theory involved clearly with each chapter devoted to a clearly identifiable control paradigm; • demonstrates convergence proofs of the ADP algorithms to deepen understanding of the derivation of stability and convergence with the iterative computational methods used; and • shows how ADP methods can be put to use both in simulation and in real applications. This text will be of considerable interest to researchers interested in optimal control and its applications in operations research, applied mathematics computational intelligence and engineering. Graduate students working in control and operations research will also find the ideas presented here to be a source of powerful methods for furthering their study.
Author: Rein Luus Publisher: Chapman and Hall/CRC ISBN: 9781584881483 Category : Mathematics Languages : en Pages : 344
Book Description
Dynamic programming is a powerful method for solving optimization problems, but has a number of drawbacks that limit its use to solving problems of very low dimension. To overcome these limitations, author Rein Luus suggested using it in an iterative fashion. Although this method required vast computer resources, modifications to his original scheme have made the computational procedure feasible. With iteration, dynamic programming becomes an effective optimization procedure for very high-dimensional optimal control problems and has demonstrated applicability to singular control problems. Recently, iterative dynamic programming (IDP) has been refined to handle inequality state constraints and noncontinuous functions. Iterative Dynamic Programming offers a comprehensive presentation of this powerful tool. It brings together the results of work carried out by the author and others - previously available only in scattered journal articles - along with the insight that led to its development. The author provides the necessary background, examines the effects of the parameters involved, and clearly illustrates IDP's advantages.
Author: Kok Lay Teo Publisher: Springer Nature ISBN: 3030699137 Category : Mathematics Languages : en Pages : 581
Book Description
The aim of this book is to furnish the reader with a rigorous and detailed exposition of the concept of control parametrization and time scaling transformation. It presents computational solution techniques for a special class of constrained optimal control problems as well as applications to some practical examples. The book may be considered an extension of the 1991 monograph A Unified Computational Approach Optimal Control Problems, by K.L. Teo, C.J. Goh, and K.H. Wong. This publication discusses the development of new theory and computational methods for solving various optimal control problems numerically and in a unified fashion. To keep the book accessible and uniform, it includes those results developed by the authors, their students, and their past and present collaborators. A brief review of methods that are not covered in this exposition, is also included. Knowledge gained from this book may inspire advancement of new techniques to solve complex problems that arise in the future. This book is intended as reference for researchers in mathematics, engineering, and other sciences, graduate students and practitioners who apply optimal control methods in their work. It may be appropriate reading material for a graduate level seminar or as a text for a course in optimal control.
Author: Daniela Tonon Publisher: Springer ISBN: 3319607715 Category : Mathematics Languages : en Pages : 399
Book Description
Focusing on applications to science and engineering, this book presents the results of the ITN-FP7 SADCO network’s innovative research in optimization and control in the following interconnected topics: optimality conditions in optimal control, dynamic programming approaches to optimal feedback synthesis and reachability analysis, and computational developments in model predictive control. The novelty of the book resides in the fact that it has been developed by early career researchers, providing a good balance between clarity and scientific rigor. Each chapter features an introduction addressed to PhD students and some original contributions aimed at specialist researchers. Requiring only a graduate mathematical background, the book is self-contained. It will be of particular interest to graduate and advanced undergraduate students, industrial practitioners and to senior scientists wishing to update their knowledge.
Author: Warren B. Powell Publisher: John Wiley & Sons ISBN: 0470182954 Category : Mathematics Languages : en Pages : 487
Book Description
A complete and accessible introduction to the real-world applications of approximate dynamic programming With the growing levels of sophistication in modern-day operations, it is vital for practitioners to understand how to approach, model, and solve complex industrial problems. Approximate Dynamic Programming is a result of the author's decades of experience working in large industrial settings to develop practical and high-quality solutions to problems that involve making decisions in the presence of uncertainty. This groundbreaking book uniquely integrates four distinct disciplines—Markov design processes, mathematical programming, simulation, and statistics—to demonstrate how to successfully model and solve a wide range of real-life problems using the techniques of approximate dynamic programming (ADP). The reader is introduced to the three curses of dimensionality that impact complex problems and is also shown how the post-decision state variable allows for the use of classical algorithmic strategies from operations research to treat complex stochastic optimization problems. Designed as an introduction and assuming no prior training in dynamic programming of any form, Approximate Dynamic Programming contains dozens of algorithms that are intended to serve as a starting point in the design of practical solutions for real problems. The book provides detailed coverage of implementation challenges including: modeling complex sequential decision processes under uncertainty, identifying robust policies, designing and estimating value function approximations, choosing effective stepsize rules, and resolving convergence issues. With a focus on modeling and algorithms in conjunction with the language of mainstream operations research, artificial intelligence, and control theory, Approximate Dynamic Programming: Models complex, high-dimensional problems in a natural and practical way, which draws on years of industrial projects Introduces and emphasizes the power of estimating a value function around the post-decision state, allowing solution algorithms to be broken down into three fundamental steps: classical simulation, classical optimization, and classical statistics Presents a thorough discussion of recursive estimation, including fundamental theory and a number of issues that arise in the development of practical algorithms Offers a variety of methods for approximating dynamic programs that have appeared in previous literature, but that have never been presented in the coherent format of a book Motivated by examples from modern-day operations research, Approximate Dynamic Programming is an accessible introduction to dynamic modeling and is also a valuable guide for the development of high-quality solutions to problems that exist in operations research and engineering. The clear and precise presentation of the material makes this an appropriate text for advanced undergraduate and beginning graduate courses, while also serving as a reference for researchers and practitioners. A companion Web site is available for readers, which includes additional exercises, solutions to exercises, and data sets to reinforce the book's main concepts.
Author: Stephen J. Kahne
Author: Stephen J. Kahne
Author: Stephen J. Kahne
Author: Dimitri Bertsekas
Author: Huaguang Zhang
Author: Rein Luus
Author: Kok Lay Teo
Author: George L. Nemhauser
Author: Daniela Tonon
Author: David H. Jacobson
Author: Warren B. Powell