1st Edition

Multi-Resolution Methods for Modeling and Control of Dynamical Systems

By Puneet Singla, John L. Junkins Copyright 2009
    316 Pages 8 Color & 120 B/W Illustrations
    by Chapman & Hall

    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.

    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.


    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