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Model Reduction of Parametrized Systems
The special volume offers a global guide to new concepts and approaches concerning the following topics: reduced basis methods, proper orthogonal decomposition, proper generalized decomposition, approximation theory related to model reduction, learning theory and compressed sensing, stochastic and high-dimensional problems, system-theoretic methods, nonlinear model reduction, reduction of coupled problems/multiphysics, optimization and optimal control, state estimation and control, reduced order models and domain decomposition methods, Krylov-subspace and interpolatory methods, and applications to real industrial and complex problems. The book represents the state of the art in the development of reduced order methods. It contains contributions from internationally respected experts, guaranteeing a wide range of expertise and topics. Further, it reflects an important effor t, carried out over the last 12 years, to build a growing research community in this field. Though not a textbook, some of the chapters can be used as reference materials or lecture notes for classes and tutorials (doctoral schools, master classes).
Approximation of Large-Scale Dynamical Systems
Mathematical models are used to simulate, and sometimes control, the behavior of physical and artificial processes such as the weather and very large-scale integration (VLSI) circuits. The increasing need for accuracy has led to the development of highly complex models. However, in the presence of limited computational accuracy and storage capabilities model reduction (system approximation) is often necessary. Approximation of Large-Scale Dynamical Systems provides a comprehensive picture of model reduction, combining system theory with numerical linear algebra and computational considerations. It addresses the issue of model reduction and the resulting trade-offs between accuracy and complexity. Special attention is given to numerical aspects, simulation questions, and practical applications.
Shapes and Geometries
The tools to use for problems where the modeling, optimization, or control variable is the structure of a geometric object.
Reduced Basis Methods for Partial Differential Equations
This book provides a basic introduction to reduced basis (RB) methods for problems involving the repeated solution of partial differential equations (PDEs) arising from engineering and applied sciences, such as PDEs depending on several parameters and PDE-constrained optimization. The book presents a general mathematical formulation of RB methods, analyzes their fundamental theoretical properties, discusses the related algorithmic and implementation aspects, and highlights their built-in algebraic and geometric structures. More specifically, the authors discuss alternative strategies for constructing accurate RB spaces using greedy algorithms and proper orthogonal decomposition techniques, i...
Peterson's Graduate Programs Programs in Mathematics 2011
Peterson's Graduate Programs in Mathematics contains a wealth of information on colleges and universities that offer graduate work in Applied Mathematics, Applied Statistics, Biomathematics, Biometry, Biostatistics, Computational Sciences, Mathematical and Computational Finance, Mathematics, and Statistics. The institutions listed include those in the United States, Canada, and abroad that are accredited by U.S. accrediting bodies. Up-to-date information, collected through Peterson's Annual Survey of Graduate and Professional Institutions, provides valuable information on degree offerings, professional accreditation, jointly offered degrees, part-time and evening/weekend programs, postbaccal...
Nonlinear Output Regulation
Nonlinear Output Regulation: Theory and Applications provides a comprehensive and in-depth treatment of the nonlinear output regulation problem. It contains up-to-date research results and algorithms and tools for approaching and solving the output regulation problem and related problems, such as robust stabilization of nonlinear systems. Output regulation is a general mathematical formulation of many control problems encountered in daily life including cruise control of automobiles, landing and takeoff of aircraft, manipulation of robot arms, orbiting of satellites, and speed regulation of motors. The book provides a self-contained treatment starting with an introduction to the linear outpu...
Extending H-infinity Control to Nonlinear Systems
H-infinity control originated from an effort to codify classical control methods, where one shapes frequency response functions for linear systems to meet certain objectives. H-infinity control underwent tremendous development in the 1980s and made considerable strides toward systematizing classical control. This book addresses the next major issue of how this extends to nonlinear systems. At the core of nonlinear control theory lie two partial differential equations (PDEs). One is a first-order evolution equation called the information state equation, which constitutes the dynamics of the controller. One can view this equation as a nonlinear dynamical system. Much of this volume is concerned with basic properties of this system, such as the nature of trajectories, stability, and, most important, how it leads to a general solution of the nonlinear H-infinity control problem.
Accelerated Universities
During the past several decades, several “highly-resourced, accelerated research universities” have been established around the world to pursue—and achieve—academic and research excellence. These institutions are entirely new, not existing universities that were reconfigured. Accelerated Universities provides case studies of eight such universities and highlights the lessons to be learned from these examples. Each of the cases is written by someone involved with leadership at the early developmental stages of each university, and provides insights that only senior executives can illustrate. Accelerated Universities shows that visionary leadership and generous funding combined with innovative ideas can yield impressive results in a short time. Universities aspiring to recognition among the top tier of global institutions will find this book indispensable.
Applied Dynamic Programming for Optimization of Dynamical Systems
Based on the results of over 10 years of research and development by the authors, this book presents a broad cross section of dynamic programming (DP) techniques applied to the optimization of dynamical systems. The main goal of the research effort was to develop a robust path planning/trajectory optimization tool that did not require an initial guess. The goal was partially met with a combination of DP and homotopy algorithms. DP algorithms are presented here with a theoretical development, and their successful application to variety of practical engineering problems is emphasized.
Advanced Mathematical Methods for Scientists and Engineers I
A clear, practical and self-contained presentation of the methods of asymptotics and perturbation theory for obtaining approximate analytical solutions to differential and difference equations. Aimed at teaching the most useful insights in approaching new problems, the text avoids special methods and tricks that only work for particular problems. Intended for graduates and advanced undergraduates, it assumes only a limited familiarity with differential equations and complex variables. The presentation begins with a review of differential and difference equations, then develops local asymptotic methods for such equations, and explains perturbation and summation theory before concluding with an exposition of global asymptotic methods. Emphasizing applications, the discussion stresses care rather than rigor and relies on many well-chosen examples to teach readers how an applied mathematician tackles problems. There are 190 computer-generated plots and tables comparing approximate and exact solutions, over 600 problems of varying levels of difficulty, and an appendix summarizing the properties of special functions.
