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Author: Puneet Singla
Publisher: CRC Press
ISBN: 9781584887706
Category : Science
Languages : en
Pages : 320
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Book Description
Unifying the most important methodology in this field, Multi-Resolution Methods for Modeling and Control of Dynamical Systems explores existing approximation methods as well as develops new ones for the approximate solution of large-scale dynamical system problems. It brings together a wide set of material from classical orthogonal function approximation, neural network input-output approximation, finite element methods for distributed parameter systems, and various approximation methods employed in adaptive control and learning theory. With sufficient rigor and generality, the book promotes a qualitative understanding of the development of key ideas. It facilitates a deep appreciation of the important nuances and restrictions implicit in the algorithms that affect the validity of the results produced. The text features benchmark problems throughout to offer insights and illustrate some of the computational implications. The authors provide a framework for understanding the advantages, drawbacks, and application areas of existing and new algorithms for input-output approximation. They also present novel adaptive learning algorithms that can be adjusted in real time to the various parameters of unknown mathematical models.
Author: Puneet Singla
Publisher: CRC Press
ISBN: 9781584887706
Category : Science
Languages : en
Pages : 320
Get Book
Book Description
Unifying the most important methodology in this field, Multi-Resolution Methods for Modeling and Control of Dynamical Systems explores existing approximation methods as well as develops new ones for the approximate solution of large-scale dynamical system problems. It brings together a wide set of material from classical orthogonal function approximation, neural network input-output approximation, finite element methods for distributed parameter systems, and various approximation methods employed in adaptive control and learning theory. With sufficient rigor and generality, the book promotes a qualitative understanding of the development of key ideas. It facilitates a deep appreciation of the important nuances and restrictions implicit in the algorithms that affect the validity of the results produced. The text features benchmark problems throughout to offer insights and illustrate some of the computational implications. The authors provide a framework for understanding the advantages, drawbacks, and application areas of existing and new algorithms for input-output approximation. They also present novel adaptive learning algorithms that can be adjusted in real time to the various parameters of unknown mathematical models.
Author: Puneet Singla
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
This dissertation introduces novel methods for solving highly challenging modeling and control problems, motivated by advanced aerospace systems. Adaptable, robust and computationally effcient, multi-resolution approximation algorithms based on Radial Basis Function Network and Global-Local Orthogonal Mapping approaches are developed to address various problems associated with the design of large scale dynamical systems. The main feature of the Radial Basis Function Network approach is the unique direction dependent scaling and rotation of the radial basis function via a novel Directed Connectivity Graph approach. The learning of shaping and rotation parameters for the Radial Basis Functions led to a broadly useful approximation approach that leads to global approximations capable of good local approximation for many moderate dimensioned applications. However, even with these refinements, many applications with many high frequency local input/output variations and a high dimensional input space remain a challenge and motivate us to investigate an entirely new approach. The Global-Local Orthogonal Mapping method is based upon a novel averaging process that allows construction of a piecewise continuous global family of local least-squares approximations, while retaining the freedom to vary in a general way the resolution (e.g., degrees of freedom) of the local approximations. These approximation methodologies are compatible with a wide variety of disciplines such as continuous function approximation, dynamic system modeling, nonlinear signal processing and time series prediction. Further, related methods are developed for the modeling of dynamical systems nominally described by nonlinear differential equations and to solve for static and dynamic response of Distributed Parameter Systems in an effcient manner. Finally, a hierarchical control allocation algorithm is presented to solve the control allocation problem for highly over-actuated systems that might arise with the development of embedded systems. The control allocation algorithm makes use of the concept of distribution functions to keep in check the "curse of dimensionality". The studies in the dissertation focus on demonstrating, through analysis, simulation, and design, the applicability and feasibility of these approximation algorithms to a variety of examples. The results from these studies are of direct utility in addressing the "curse of dimensionality" and frequent redundancy of neural network approximation.
Author: Leonard David Berkovitz
Publisher: CRC Press
ISBN: 1466560266
Category : Mathematics
Languages : en
Pages : 394
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Book Description
Nonlinear Optimal Control Theory presents a deep, wide-ranging introduction to the mathematical theory of the optimal control of processes governed by ordinary differential equations and certain types of differential equations with memory. Many examples illustrate the mathematical issues that need to be addressed when using optimal control techniques in diverse areas. Drawing on classroom-tested material from Purdue University and North Carolina State University, the book gives a unified account of bounded state problems governed by ordinary, integrodifferential, and delay systems. It also discusses Hamilton-Jacobi theory. By providing a sufficient and rigorous treatment of finite dimensional control problems, the book equips readers with the foundation to deal with other types of control problems, such as those governed by stochastic differential equations, partial differential equations, and differential games.
Author: John A. Burns
Publisher: CRC Press
ISBN: 146657139X
Category : Mathematics
Languages : en
Pages : 564
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Book Description
Introduction to the Calculus of Variations and Control with Modern Applications provides the fundamental background required to develop rigorous necessary conditions that are the starting points for theoretical and numerical approaches to modern variational calculus and control problems. The book also presents some classical sufficient conditions and discusses the importance of distinguishing between the necessary and sufficient conditions. In the first part of the text, the author develops the calculus of variations and provides complete proofs of the main results. He explains how the ideas behind the proofs are essential to the development of modern optimization and control theory. Focusing on optimal control problems, the second part shows how optimal control is a natural extension of the classical calculus of variations to more complex problems. By emphasizing the basic ideas and their mathematical development, this book gives you the foundation to use these mathematical tools to then tackle new problems. The text moves from simple to more complex problems, allowing you to see how the fundamental theory can be modified to address more difficult and advanced challenges. This approach helps you understand how to deal with future problems and applications in a realistic work environment.
Author: John L. Crassidis
Publisher: CRC Press
ISBN: 1439839867
Category : Mathematics
Languages : en
Pages : 745
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Book Description
Optimal Estimation of Dynamic Systems, Second Edition highlights the importance of both physical and numerical modeling in solving dynamics-based estimation problems found in engineering systems. Accessible to engineering students, applied mathematicians, and practicing engineers, the text presents the central concepts and methods of optimal estima
Author: Stephen J. Kirkland
Publisher: CRC Press
ISBN: 1439888582
Category : Mathematics
Languages : en
Pages : 334
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Book Description
Group inverses for singular M-matrices are useful tools not only in matrix analysis, but also in the analysis of stochastic processes, graph theory, electrical networks, and demographic models. Group Inverses of M-Matrices and Their Applications highlights the importance and utility of the group inverses of M-matrices in several application areas. After introducing sample problems associated with Leslie matrices and stochastic matrices, the authors develop the basic algebraic and spectral properties of the group inverse of a general matrix. They then derive formulas for derivatives of matrix functions and apply the formulas to matrices arising in a demographic setting, including the class of Leslie matrices. With a focus on Markov chains, the text shows how the group inverse of an appropriate M-matrix is used in the perturbation analysis of the stationary distribution vector as well as in the derivation of a bound for the asymptotic convergence rate of the underlying Markov chain. It also illustrates how to use the group inverse to compute and analyze the mean first passage matrix for a Markov chain. The final chapters focus on the Laplacian matrix for an undirected graph and compare approaches for computing the group inverse. Collecting diverse results into a single volume, this self-contained book emphasizes the connections between problems arising in Markov chains, Perron eigenvalue analysis, and spectral graph theory. It shows how group inverses offer valuable insight into each of these areas.
Author: Matthew P. Coleman
Publisher: CRC Press
ISBN: 1439898472
Category : Mathematics
Languages : en
Pages : 670
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Book Description
An Introduction to Partial Differential Equations with MATLAB, Second Edition illustrates the usefulness of PDEs through numerous applications and helps students appreciate the beauty of the underlying mathematics. Updated throughout, this second edition of a bestseller shows students how PDEs can model diverse problems, including the flow of heat,
Author: Victor Shapiro
Publisher: CRC Press
ISBN: 1439854289
Category : Mathematics
Languages : en
Pages : 352
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Book Description
Fourier Series in Several Variables with Applications to Partial Differential Equations illustrates the value of Fourier series methods in solving difficult nonlinear partial differential equations (PDEs). Using these methods, the author presents results for stationary Navier-Stokes equations, nonlinear reaction-diffusion systems, and quasilinear e
Author: Zhi Zong
Publisher: CRC Press
ISBN: 9781420082494
Category : Science
Languages : en
Pages : 362
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Book Description
Modern Tools to Perform Numerical Differentiation The original direct differential quadrature (DQ) method has been known to fail for problems with strong nonlinearity and material discontinuity as well as for problems involving singularity, irregularity, and multiple scales. But now researchers in applied mathematics, computational mechanics, and engineering have developed a range of innovative DQ-based methods to overcome these shortcomings. Advanced Differential Quadrature Methods explores new DQ methods and uses these methods to solve problems beyond the capabilities of the direct DQ method. After a basic introduction to the direct DQ method, the book presents a number of DQ methods, including complex DQ, triangular DQ, multi-scale DQ, variable order DQ, multi-domain DQ, and localized DQ. It also provides a mathematical compendium that summarizes Gauss elimination, the Runge–Kutta method, complex analysis, and more. The final chapter contains three codes written in the FORTRAN language, enabling readers to quickly acquire hands-on experience with DQ methods. Focusing on leading-edge DQ methods, this book helps readers understand the majority of journal papers on the subject. In addition to gaining insight into the dynamic changes that have recently occurred in the field, readers will quickly master the use of DQ methods to solve complex problems.
Author: Mark McKibben
Publisher: CRC Press
ISBN: 142009212X
Category : Mathematics
Languages : en
Pages : 463
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Book Description
Most existing books on evolution equations tend either to cover a particular class of equations in too much depth for beginners or focus on a very specific research direction. Thus, the field can be daunting for newcomers to the field who need access to preliminary material and behind-the-scenes detail. Taking an applications-oriented, conversational approach, Discovering Evolution Equations with Applications: Volume 2-Stochastic Equations provides an introductory understanding of stochastic evolution equations. The text begins with hands-on introductions to the essentials of real and stochastic analysis. It then develops the theory for homogenous one-dimensional stochastic ordinary differential equations (ODEs) and extends the theory to systems of homogenous linear stochastic ODEs. The next several chapters focus on abstract homogenous linear, nonhomogenous linear, and semi-linear stochastic evolution equations. The author also addresses the case in which the forcing term is a functional before explaining Sobolev-type stochastic evolution equations. The last chapter discusses several topics of active research. Each chapter starts with examples of various models. The author points out the similarities of the models, develops the theory involved, and then revisits the examples to reinforce the theoretical ideas in a concrete setting. He incorporates a substantial collection of questions and exercises throughout the text and provides two layers of hints for selected exercises at the end of each chapter. Suitable for readers unfamiliar with analysis even at the undergraduate level, this book offers an engaging and accessible account of core theoretical results of stochastic evolution equations in a way that gradually builds readers’ intuition.
