Optimal Design And Control
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| Author | : Friedrich Pukelsheim |
| Publisher | : SIAM |
| Total Pages | : 527 |
| Release | : 2006-04-01 |
| Genre | : Mathematics |
| ISBN | : 0898716047 |
Optimal Design of Experiments offers a rare blend of linear algebra, convex analysis, and statistics. The optimal design for statistical experiments is first formulated as a concave matrix optimization problem. Using tools from convex analysis, the problem is solved generally for a wide class of optimality criteria such as D-, A-, or E-optimality. The book then offers a complementary approach that calls for the study of the symmetry properties of the design problem, exploiting such notions as matrix majorization and the Kiefer matrix ordering. The results are illustrated with optimal designs for polynomial fit models, Bayes designs, balanced incomplete block designs, exchangeable designs on the cube, rotatable designs on the sphere, and many other examples.
| Author | : Jeff Borggaard |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 298 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461208394 |
This volume is the proceedings of the Workshop on Optimal Design and Control that was held in Blacksburg, Virginia, April 8-9, 1994. The workshop was spon sored by the Air Force Office of Scientific Research through the Air Force Center for Optimal Design and Control (CODAC) at Virginia Tech. The workshop was a gathering of engineers and mathematicians actively in volved in innovative research in control and optimization, with emphasis placed on problems governed by partial differential equations. The interdisciplinary nature of the workshop and the wide range of subdisciplines represented by the partici pants enabled an exchange of valuable information and also led to significant dis cussions about multidisciplinary optimization issues. One of the goals of the work shop was to include laboratory, industrial, and academic researchers so that anal yses, algorithms, implementations, and applications could all be well-represented in the talks; this interdisciplinary nature is reflected in these proceedings. An overriding impression that can be gleaned from the papers in this volume is the complexity of problems addressed by not only those authors engaged in appli cations, but also by those engaged in algorithmic development and even mathemat ical analyses. Thus, in many instances, systematic approaches using fully nonlin ear constraint equations are routinely used to solve control and optimization prob lems, in some cases replacing ad-hoc or empirically based procedures.
| Author | : S. Silvey |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 94 |
| Release | : 2013-03-09 |
| Genre | : Science |
| ISBN | : 9400959125 |
Prior to the 1970's a substantial literature had accumulated on the theory of optimal design, particularly of optimal linear regression design. To a certain extent the study of the subject had been piecemeal, different criteria of optimality having been studied separately. Also to a certain extent the topic was regarded as being largely of theoretical interest and as having little value for the practising statistician. However during this decade two significant developments occurred. It was observed that the various different optimality criteria had several mathematical properties in common; and general algorithms for constructing optimal design measures were developed. From the first of these there emerged a general theory of remarkable simplicity and the second at least raised the possibility that the theory would have more practical value. With respect to the second point there does remain a limiting factor as far as designs that are optimal for parameter estimation are concerned, and this is that the theory assumes that the model be collected is known a priori. This of course underlying data to is seldom the case in practice and it often happens that designs which are optimal for parameter estimation allow no possibility of model validation. For this reason the theory of design for parameter estimation may well have to be combined with a theory of model validation before its practical potential is fully realized. Nevertheless discussion in this monograph is limited to the theory of design optimal for parameter estimation.
| Author | : Panos Y. Papalambros |
| Publisher | : Cambridge University Press |
| Total Pages | : 416 |
| Release | : 2000-07-10 |
| Genre | : Mathematics |
| ISBN | : 9780521627276 |
Principles of Optimal Design puts the concept of optimal design on a rigorous foundation and demonstrates the intimate relationship between the mathematical model that describes a design and the solution methods that optimize it. Since the first edition was published, computers have become ever more powerful, design engineers are tackling more complex systems, and the term optimization is now routinely used to denote a design process with increased speed and quality. This second edition takes account of these developments and brings the original text thoroughly up to date. The book now includes a discussion of trust region and convex approximation algorithms. A new chapter focuses on how to construct optimal design models. Three new case studies illustrate the creation of optimization models. The final chapter on optimization practice has been expanded to include computation of derivatives, interpretation of algorithmic results, and selection of algorithms and software. Both students and practising engineers will find this book a valuable resource for design project work.
| Author | : Kirti R. Shah |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 179 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461236622 |
There has been an enormous growth in recent years in the literature on discrete optimal designs. The optimality problems have been formulated in various models arising in the experimental designs and substantial progress has been made towards solving some of these. The subject has now reached a stage of completeness which calls for a self-contained monograph on this topic. The aim of this monograph is to present the state of the art and to focus on more recent advances in this rapidly developing area. We start with a discussion of statistical optimality criteria in Chapter One. Chapters Two and Three deal with optimal block designs. Row-column designs are dealt with in Chapter Four. In Chapter Five we deal with optimal designs with mixed effects models. Repeated measurement designs are considered in Chapter Six. Chapter Seven deals with some special situations and Weighing designs are dis cussed in Chapter Eight. We have endeavoured to include all the major developments that have taken place in the last three decades. The book should be of use to research workers in several areas including combinatorics as well as to the experimenters in diverse fields of applications. Since the details of the construction of the designs are available in excellent books, we have only pointed out the designs which have optimality proper ties. We believe, this will be adequate for the experimenters.
| Author | : Feng Lin |
| Publisher | : John Wiley & Sons |
| Total Pages | : 378 |
| Release | : 2007-09-27 |
| Genre | : Science |
| ISBN | : 9780470059562 |
Comprehensive and accessible guide to the three main approaches to robust control design and its applications Optimal control is a mathematical field that is concerned with control policies that can be deduced using optimization algorithms. The optimal control approach to robust control design differs from conventional direct approaches to robust control that are more commonly discussed by firstly translating the robust control problem into its optimal control counterpart, and then solving the optimal control problem. Robust Control Design: An Optimal Control Approach offers a complete presentation of this approach to robust control design, presenting modern control theory in an concise manner. The other two major approaches to robust control design, the H_infinite approach and the Kharitonov approach, are also covered and described in the simplest terms possible, in order to provide a complete overview of the area. It includes up-to-date research, and offers both theoretical and practical applications that include flexible structures, robotics, and automotive and aircraft control. Robust Control Design: An Optimal Control Approach will be of interest to those needing an introductory textbook on robust control theory, design and applications as well as graduate and postgraduate students involved in systems and control research. Practitioners will also find the applications presented useful when solving practical problems in the engineering field.
| Author | : Michael J. Grimble |
| Publisher | : John Wiley & Sons |
| Total Pages | : 698 |
| Release | : 2006-05-01 |
| Genre | : Science |
| ISBN | : 0470020741 |
Robust Industrial Control Systems: Optimal Design Approach for Polynomial Systems presents a comprehensive introduction to the use of frequency domain and polynomial system design techniques for a range of industrial control and signal processing applications. The solution of stochastic and robust optimal control problems is considered, building up from single-input problems and gradually developing the results for multivariable design of the later chapters. In addition to cataloguing many of the results in polynomial systems needed to calculate industrial controllers and filters, basic design procedures are also introduced which enable cost functions and system descriptions to be specified in order to satisfy industrial requirements. Providing a range of solutions to control and signal processing problems, this book: * Presents a comprehensive introduction to the polynomial systems approach for the solution of H_2 and H_infinity optimal control problems. * Develops robust control design procedures using frequency domain methods. * Demonstrates design examples for gas turbines, marine systems, metal processing, flight control, wind turbines, process control and manufacturing systems. * Includes the analysis of multi-degrees of freedom controllers and the computation of restricted structure controllers that are simple to implement. * Considers time-varying control and signal processing problems. * Addresses the control of non-linear processes using both multiple model concepts and new optimal control solutions. Robust Industrial Control Systems: Optimal Design Approach for Polynomial Systems is essential reading for professional engineers requiring an introduction to optimal control theory and insights into its use in the design of real industrial processes. Students and researchers in the field will also find it an excellent reference tool.
| Author | : Shaler Stidham Jr. |
| Publisher | : CRC Press |
| Total Pages | : 385 |
| Release | : 2009-03-27 |
| Genre | : Business & Economics |
| ISBN | : 142001000X |
The First Comprehensive Book on the SubjectFocusing on the underlying structure of a system, Optimal Design of Queueing Systems explores how to set the parameters of a queueing system, such as arrival and service rates, before putting it into operation. It considers various objectives, comparing individually optimal (Nash equilibrium), socially opt
| Author | : Urmila Diwekar |
| Publisher | : CRC Press |
| Total Pages | : 402 |
| Release | : 2011-12-21 |
| Genre | : Science |
| ISBN | : 1439861226 |
Most available books in chemical engineering mainly pertain to continuous processes, with batch distillation relegated to a small section. Filling this void in the chemical engineering literature, Batch Distillation: Simulation, Optimal Design, and Control, Second Edition helps readers gain a solid, hands-on background in batch processing. The second edition of this bestseller explores numerous new developments in batch distillation that have emerged since the publication of the first edition. New to the Second Edition Special sections on complex column configurations and azeotropic, extractive, and reactive distillation A chapter on various kinds of uncertainties in batch distillation A chapter covering software packages for batch distillation simulation, design, optimization, and control Separate chapters on complex columns and complex systems Up-to-date references and coverage of recent research articles This edition continues to explain how to effectively design, synthesize, and make operations decisions related to batch processes. Through careful treatments of uncertainty analysis, optimization, and optimal control methods, the author gives readers the necessary tools for making the best decisions in practice. While primarily designed for a graduate course in batch distillation, the text can also be used in undergraduate chemical engineering courses. In addition, researchers and academics faced with batch distillation research problems and practicing chemical engineers tackling problems in actual day-to-day operations will find the book to be a useful reference source.
| Author | : Herman Chernoff |
| Publisher | : SIAM |
| Total Pages | : 124 |
| Release | : 1972-01-01 |
| Genre | : Technology & Engineering |
| ISBN | : 9781611970593 |
An exploration of the interrelated fields of design of experiments and sequential analysis with emphasis on the nature of theoretical statistics and how this relates to the philosophy and practice of statistics.
