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

Multi-Resolution Methods for Modeling and Control of Dynamical Systems

1st Edition

By Puneet Singla, John L. Junkins

Chapman and Hall/CRC

320 pages | 8 Color Illus. | 120 B/W Illus.

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Hardback: 9781584887690
pub: 2008-08-01
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pub: 2008-08-01
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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.


"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

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.

About the Originator

About the Series

Chapman & Hall/CRC Applied Mathematics & Nonlinear Science

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Subject Categories

BISAC Subject Codes/Headings:
SCIENCE / Mechanics / General