Multi-Resolution Methods for Modeling and Control of Dynamical Systems  book cover
1st Edition

Multi-Resolution Methods for Modeling and Control of Dynamical Systems

ISBN 9781584887690
Published August 1, 2008 by Chapman & Hall
320 Pages 8 Color & 120 B/W Illustrations

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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.

Table of Contents

Least Square Methods
The Least Square Algorithm
Linear Least Square Methods
Nonlinear Least Squares Algorithm
Properties of Least Square Algorithms
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
Direction-Dependent Approach
Directed Connectivity Graph
Modified Minimal Resource Allocating Algorithm (MMRAN)
Numerical Simulation Examples
Multi-Resolution Approximation Methods
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
Each chapter contains an Introduction and a Summary.

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"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