Singla / Junkins Multi-Resolution Methods for Modeling and Control of Dynamical Systems

1. Auflage 2010
ISBN: 978-1-58488-770-6
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 320 Seiten

Reihe: Chapman & Hall/CRC Applied Mathematics & Nonlinear Science

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.

Zielgruppe

Aerospace, mechanical, civil, and electrical engineers; applied mathematicians

Autoren/Hrsg.

Singla, Puneet

Junkins, John L.

Fachgebiete

• Naturwissenschaften Physik Mechanik

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.