1st Edition
Multi-Resolution Methods for Modeling and Control of Dynamical Systems
316 Pages
8 Color & 120 B/W Illustrations
by
Chapman & Hall
320 Pages
by
Chapman & Hall
Also available as eBook on:
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... Read more
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.
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.
Biography
Puneet Singla, John L. Junkins
"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
