Download or read book Directions in Mathematical Systems Theory and Optimization written by Anders Rantzer and published by Springer. This book was released on 2003-07-01 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: For more than three decades, Anders Lindquist has delivered fundamental cont- butions to the ?elds of systems, signals and control. Throughout this period, four themes can perhaps characterize his interests: Modeling, estimation and ?ltering, feedback and robust control. His contributions to modeling include seminal work on the role of splitting subspaces in stochastic realization theory, on the partial realization problem for both deterministic and stochastic systems, on the solution of the rational covariance extension problem and on system identi?cation. His contributions to ?ltering and estimation include the development of fast ?ltering algorithms, leading to a nonlinear dynamical system which computes spectral factors in its steady state, and which provide an alternate, linear in the dimension of the state space, to computing the Kalman gain from a matrix Riccati equation. His further research on the phase portrait of this dynamical system gave a better understanding of when the Kalman ?lter will converge, answering an open question raised by Kalman. While still a student he established the separation principle for stochastic function differential equations, including some fundamental work on optimal control for stochastic systems with time lags. He continued his interest in feedback control by deriving optimal and robust control feedback laws for suppressing the effects of harmonic disturbances. Moreover, his recent work on a complete parameterization of all rational solutions to the Nevanlinna-Pick problem is providing a new approach to robust control design.

Download or read book Optimization of Elliptic Systems written by Pekka Neittaanmaki and published by Springer Science & Business Media. This book was released on 2007-01-04 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present monograph is intended to provide a comprehensive and accessible introduction to the optimization of elliptic systems. This area of mathematical research, which has many important applications in science and technology. has experienced an impressive development during the past two decades. There are already many good textbooks dealing with various aspects of optimal design problems. In this regard, we refer to the works of Pironneau [1984], Haslinger and Neittaanmaki [1988], [1996], Sokolowski and Zolksio [1992], Litvinov [2000], Allaire [2001], Mohammadi and Pironneau [2001], Delfour and Zolksio [2001], and Makinen and Haslinger [2003]. Already Lions [I9681 devoted a major part of his classical monograph on the optimal control of partial differential equations to the optimization of elliptic systems. Let us also mention that even the very first known problem of the calculus of variations, the brachistochrone studied by Bernoulli back in 1696. is in fact a shape optimization problem. The natural richness of this mathematical research subject, as well as the extremely large field of possible applications, has created the unusual situation that although many important results and methods have already been est- lished, there are still pressing unsolved questions. In this monograph, we aim to address some of these open problems; as a consequence, there is only a minor overlap with the textbooks already existing in the field.

Download or read book Mathematical Theory of Optimization written by Ding-Zhu Du and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the mathematical theory of optimization. It emphasizes the convergence theory of nonlinear optimization algorithms and applications of nonlinear optimization to combinatorial optimization. Mathematical Theory of Optimization includes recent developments in global convergence, the Powell conjecture, semidefinite programming, and relaxation techniques for designs of approximation solutions of combinatorial optimization problems.

Download or read book Optimization and Dynamical Systems written by Uwe Helmke and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work is aimed at mathematics and engineering graduate students and researchers in the areas of optimization, dynamical systems, control sys tems, signal processing, and linear algebra. The motivation for the results developed here arises from advanced engineering applications and the emer gence of highly parallel computing machines for tackling such applications. The problems solved are those of linear algebra and linear systems the ory, and include such topics as diagonalizing a symmetric matrix, singular value decomposition, balanced realizations, linear programming, sensitivity minimization, and eigenvalue assignment by feedback control. The tools are those, not only of linear algebra and systems theory, but also of differential geometry. The problems are solved via dynamical sys tems implementation, either in continuous time or discrete time , which is ideally suited to distributed parallel processing. The problems tackled are indirectly or directly concerned with dynamical systems themselves, so there is feedback in that dynamical systems are used to understand and optimize dynamical systems. One key to the new research results has been the recent discovery of rather deep existence and uniqueness results for the solution of certain matrix least squares optimization problems in geomet ric invariant theory. These problems, as well as many other optimization problems arising in linear algebra and systems theory, do not always admit solutions which can be found by algebraic methods.

Download or read book Mathematical Systems Theory I written by Diederich Hinrichsen and published by Springer Science & Business Media. This book was released on 2011-08-03 with total page 818 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the mathematical foundations of systems theory in a self-contained, comprehensive, detailed and mathematically rigorous way. It is devoted to the analysis of dynamical systems and combines features of a detailed introductory textbook with that of a reference source. The book contains many examples and figures illustrating the text which help to bring out the intuitive ideas behind the mathematical constructions.

Download or read book Optimization and Control of Bilinear Systems written by Panos M. Pardalos and published by Springer Science & Business Media. This book was released on 2010-03-14 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covers developments in bilinear systems theory Focuses on the control of open physical processes functioning in a non-equilibrium mode Emphasis is on three primary disciplines: modern differential geometry, control of dynamical systems, and optimization theory Includes applications to the fields of quantum and molecular computing, control of physical processes, biophysics, superconducting magnetism, and physical information science

Download or read book Mathematical Control Theory written by Eduardo D. Sontag and published by Springer Science & Business Media. This book was released on 2013-11-21 with total page 543 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geared primarily to an audience consisting of mathematically advanced undergraduate or beginning graduate students, this text may additionally be used by engineering students interested in a rigorous, proof-oriented systems course that goes beyond the classical frequency-domain material and more applied courses. The minimal mathematical background required is a working knowledge of linear algebra and differential equations. The book covers what constitutes the common core of control theory and is unique in its emphasis on foundational aspects. While covering a wide range of topics written in a standard theorem/proof style, it also develops the necessary techniques from scratch. In this second edition, new chapters and sections have been added, dealing with time optimal control of linear systems, variational and numerical approaches to nonlinear control, nonlinear controllability via Lie-algebraic methods, and controllability of recurrent nets and of linear systems with bounded controls.

Download or read book A Mathematical View of Interior Point Methods in Convex Optimization written by James Renegar and published by SIAM. This book was released on 2001-01-01 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: Takes the reader who knows little of interior-point methods to within sight of the research frontier.

Download or read book Computational Optimization of Systems Governed by Partial Differential Equations written by Alfio Borzi and published by SIAM. This book was released on 2011-01-01 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book fills a gap between theory-oriented investigations in PDE-constrained optimization and the practical demands made by numerical solutions of PDE optimization problems. The authors discuss computational techniques representing recent developments that result from a combination of modern techniques for the numerical solution of PDEs and for sophisticated optimization schemes. The book offers readers a combined treatment of PDE-constrained optimization and uncertainties and an extensive discussion of multigrid optimization. It provides a bridge between continuous optimization and PDE modeling and focuses on the numerical solution of the corresponding problems.

Download or read book Research Directions in Distributed Parameter Systems written by Ralph C. Smith and published by SIAM. This book was released on 2003-01-01 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by the plenary speakers for the Conference on Future Directions in Distributed Parameter Systems (October 2000), the volume addresses the state of the art, open questions, and important research directions in applications modeled by partial differential equations and delay systems. Topics include electromagnetic theory for dielectric and conductive materials, flow control, cardiovascular and respiratory models, homogenization and systems theory, optimal and geometric control, reduced-order models for large-scale systems, smart materials, and nondestructive evaluation and structural health monitoring for systems, including nuclear power plants.

Download or read book Practical Mathematical Optimization written by Jan Snyman and published by Springer Science & Business Media. This book was released on 2005-03-03 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents basic optimization principles and gradient-based algorithms to a general audience, in a brief and easy-to-read form. It enables professionals to apply optimization theory to engineering, physics, chemistry, or business economics.

Download or read book An Introduction to Optimal Control Problems in Life Sciences and Economics written by Sebastian Aniţa and published by Springer Science & Business Media. This book was released on 2011-05-05 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combining control theory and modeling, this textbook introduces and builds on methods for simulating and tackling concrete problems in a variety of applied sciences. Emphasizing "learning by doing," the authors focus on examples and applications to real-world problems. An elementary presentation of advanced concepts, proofs to introduce new ideas, and carefully presented MATLAB® programs help foster an understanding of the basics, but also lead the way to new, independent research. With minimal prerequisites and exercises in each chapter, this work serves as an excellent textbook and reference for graduate and advanced undergraduate students, researchers, and practitioners in mathematics, physics, engineering, computer science, as well as biology, biotechnology, economics, and finance.

Download or read book Optimal Control Novel Directions and Applications written by Daniela Tonon and published by Springer. This book was released on 2017-09-01 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Theory of Vector Optimization written by Dinh The Luc and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 183 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes grew out of a series of lectures given by the author at the Univer sity of Budapest during 1985-1986. Additional results have been included which were obtained while the author was at the University of Erlangen-Niirnberg under a grant of the Alexander von Humboldt Foundation. Vector optimization has two main sources coming from economic equilibrium and welfare theories of Edgeworth (1881) and Pareto (1906) and from mathemat ical backgrounds of ordered spaces of Cantor (1897) and Hausdorff (1906). Later, game theory of Borel (1921) and von Neumann (1926) and production theory of Koopmans (1951) have also contributed to this area. However, only in the fifties, after the publication of Kuhn-Tucker's paper (1951) on the necessary and sufficient conditions for efficiency, and of Deubreu's paper (1954) on valuation equilibrium and Pareto optimum, has vector optimization been recognized as a mathematical discipline. The stretching development of this field began later in the seventies and eighties. Today there are a number of books on vector optimization. Most of them are concerned with the methodology and the applications. Few of them offer a systematic study of the theoretical aspects. The aim of these notes is to pro vide a unified background of vector optimization,with the emphasis on nonconvex problems in infinite dimensional spaces ordered by convex cones. The notes are arranged into six chapters. The first chapter presents prelim inary material.

Download or read book Matrix Numerical and Optimization Methods in Science and Engineering written by Kevin W. Cassel and published by Cambridge University Press. This book was released on 2021-03-04 with total page 728 pages. Available in PDF, EPUB and Kindle. Book excerpt: Address vector and matrix methods necessary in numerical methods and optimization of linear systems in engineering with this unified text. Treats the mathematical models that describe and predict the evolution of our processes and systems, and the numerical methods required to obtain approximate solutions. Explores the dynamical systems theory used to describe and characterize system behaviour, alongside the techniques used to optimize their performance. Integrates and unifies matrix and eigenfunction methods with their applications in numerical and optimization methods. Consolidating, generalizing, and unifying these topics into a single coherent subject, this practical resource is suitable for advanced undergraduate students and graduate students in engineering, physical sciences, and applied mathematics.

Download or read book Progress in Optimization written by Xiaoqi Yang and published by Springer Science & Business Media. This book was released on 2000-04-30 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second in a series of contributed, refereed volumes devoted to research in optimization by Australian researchers and their collaborators. These volumes are intended to have wide scope and include survey papers by established researchers providing up-to-date information on research directions. This volume includes survey and research papers on theories and methods of nonlinear programming, nonconvex and discrete optimization, stochastic linear programming, generalized convexity, complementarity and vector variational inequality problems, dynamic systems and optimal control and applications to traffic assignment models, train control, manufacturing systems and substrate diffusion of cutaneous tissue. Audience: Practitioners, postgraduate students and researchers in optimization.

Download or read book P graphs for Process Systems Engineering written by Ferenc Friedler and published by Springer Nature. This book was released on 2022-02-03 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses the P-graph framework for developing and understanding effective design tools for process systems engineering, and addresses the current state of its theory and applications. The book details the new philosophy of the axioms-based mathematical modelling of processing systems, the basic algorithms, areas of application, future directions, and the proofs of theorems and algorithms. Because of the rigorous foundation of the theory, the framework provides a firm basis for future research in mathematical modelling, optimization, and design of complex engineering systems. The various P-graph applications discussed include process network synthesis, reliability engineering, and systems resilience. The framework opens new avenues for research in complex systems including redundant operations for critical infrastructure, systems sustainability, and modelling tools for disaster engineering. Demonstration software is provided to facilitate the understanding of the theory. The book will be of interest to institutions, companies, and individuals performing research and R&D in process systems engineering.