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Zusatztext "Unifying important methodology in the field! this book explores existing approximation methods and develops new ones for the approximate solution of large-scale dynamical system problems." - Mechanical Engineering ASME! Vol. 131! No. 3! March 2009"This is very valuable book! edited very carefully! with hard cover and color figures in Appendix." - Ryszard Gessing! in Zentralblatt Math! 2009 Informationen zum Autor Puneet Singla, John L. Junkins Klappentext Multi-Resolution Methods for Modeling and Control of Dynamical Systems discusses the underlying principles of input/output data approximation and issues associated with modeling large-scale dynamical systems. A number of techniques are applied that cover classical finite element methods! adaptive control! and neural networks to solve various problems in engineering disciplines. The book presents these diverse topics in an integrated manner derived from dynamical systems! estimation! optimization! and approximation theory. It also provides MATLAB(R) code throughout. Zusammenfassung Presents many approaches to solve a range of engineering problems. This book develops underlying approximation theory from first principles, building a foundation on which modern approximation methods can be broadly formulated. It compares competing solutions of benchmark problems to provide a qualitative appreciation of several approaches. Inhaltsverzeichnis Least Square Methods The Least Square Algorithm Linear Least Square Methods Nonlinear Least Squares Algorithm Properties of Least Square Algorithms Examples Polynomial Approximation Gram-Schmidt Procedure of Orthogonalization Hypergeometric Function Approach to Generate Orthogonal Polynomials Discrete Variable Orthogonal Polynomials Approximation Properties of Orthogonal Polynomials Artificial Neural Networks for Input-Output Approximation Introduction Direction-Dependent Approach Directed Connectivity Graph Modified Minimal Resource Allocating Algorithm (MMRAN) Numerical Simulation Examples Multi-Resolution Approximation Methods Wavelets Bèzier Spline Moving Least Squares Method Adaptive Multi-Resolution Algorithm Numerical Results Global-Local Orthogonal Polynomial MAPping (GLO-MAP) in N Dimensions Basic Ideas Approximation in 1! 2! and N Dimensions Using Weighting Functions Global-Local Orthogonal Approximation in 1-! 2-! and N-Dimensional Spaces Algorithm Implementation Properties of GLO-MAP Approximation Illustrative Engineering Applications Nonlinear System Identification Problem Statement and Background Novel System Identification Algorithm Nonlinear System Identification Algorithm Numerical Simulation Distributed Parameter Systems MLPG-Moving Least Squares Approach Partition of Unity Finite Element Method Control Distribution for Over-Actuated Systems Problem Statement and Background Control Distribution Functions Hierarchical Control Distribution Algorithm Numerical Results Appendix References Index Each chapter contains an Introduction and a Summary. ...
