1st Edition

Nonlinear H-Infinity Control, Hamiltonian Systems and Hamilton-Jacobi Equations

By M.D.S. Aliyu Copyright 2011
    408 Pages 30 B/W Illustrations
    by CRC Press

    406 Pages 30 B/W Illustrations
    by CRC Press

    A comprehensive overview of nonlinear Hcontrol theory for both continuous-time and discrete-time systems, Nonlinear H-Control, Hamiltonian Systems and Hamilton-Jacobi Equations covers topics as diverse as singular nonlinear H-control, nonlinear H -filtering, mixed H2/ H-nonlinear control and filtering, nonlinear H-almost-disturbance-decoupling,

    and algorithms for solving the ubiquitous Hamilton-Jacobi-Isaacs equations. The link between the subject and analytical mechanics as well as the theory of partial differential equations is also elegantly summarized in a single chapter.

    Recent progress in developing computational schemes for solving the Hamilton-Jacobi equation (HJE) has facilitated the application of Hamilton-Jacobi theory in both mechanics and control. As there is currently no efficient systematic analytical or numerical approach for solving them, the biggest bottle-neck to the practical application of the nonlinear equivalent of the H-control theory has been the difficulty in solving the Hamilton-Jacobi-Isaacs partial differential-equations (or inequalities). In light of this challenge, the author hopes to inspire continuing research and discussion on this topic via examples and simulations, as well as helpful notes and a rich bibliography.

    Nonlinear H-Control, Hamiltonian Systems and Hamilton-Jacobi Equations was written for practicing professionals, educators, researchers and graduate students in electrical, computer, mechanical, aeronautical, chemical, instrumentation, industrial and systems engineering, as well as applied mathematics, economics and management.

    Introduction
    Historical Perspective on Nonlinear H-Control
    General Set-Up for Nonlinear H-Control Problems
    Notations and Preliminaries

    Basics of Differential Games
    Dynamic Programming Principle
    Discrete-Time Nonzero-Sum Dynamic Games
    Continuous-Time Nonzero-Sum Dynamic Games

    Theory of Dissipative Systems
    Dissipativity of Continuous-Time Nonlinear Systems
    l2-Gain Analysis for Continuous-Time Dissipative Systems
    Continuous-Time Passive Systems
    Feedback-Equivalence to a Passive Continuous-Time Nonlinear System
    Dissipativity and Passive Properties of Discrete-Time Nonlinear Systems
    l2-Gain Analysis for Discrete-Time Dissipative Systems
    Feedback-Equivalence to a Discrete-Time Lossless Nonlinear System

    Hamiltonian Mechanics and Hamilton-Jacobi Theory
    The Hamiltonian Formulation of Mechanics
    Canonical Transformation
    The Theory of Nonlinear Lattices
    The Method of Characteristics for First-Order Partial-Differential Equations
    Legendre Transform and Hopf-Lax Formula

    State-Feedback Nonlinear H-Control for Continuous-Time Systems
    State-Feedback H-Control for Affine Nonlinear Systems
    State-Feedback Nonlinear H Tracking Control
    Robust Nonlinear H State-Feedback Control
    State-Feedback H-Control for Time-Varying Affine Nonlinear Systems
    State-Feedback H-Control for State-Delayed Affine Nonlinear Systems
    State-Feedback H-Control for a General Class of Nonlinear Systems
    Nonlinear H Almost-Disturbance-Decoupling

    Output-Feedback Nonlinear H-Control for Continuous-Time Systems
    Output Measurement-Feedback H-Control for Affine Nonlinear Systems
    Output Measurement-Feedback Nonlinear H Tracking Control
    Robust Output Measurement-Feedback Nonlinear H-Control
    Output Measurement-Feedback H-Control for a General Class of Nonlinear Systems
    Static Output-Feedback Control for Affine Nonlinear Systems

    Discrete-Time Nonlinear H-Control
    Full-Information H-Control for Affine Nonlinear Discrete-Time Systems
    Output Measurement-Feedback Nonlinear H-Control for Affine Discrete-Time Systems
    Extensions to a General Class of Discrete-Time Nonlinear Systems
    Approximate Approach to the Discrete-Time Nonlinear H-Control Problem

    Nonlinear H-Filtering
    Continuous-Time Nonlinear H-Filtering
    Continuous-Time Robust Nonlinear H-Filtering
    Certainty-Equivalent Filters (CEFs)
    Discrete-Time Nonlinear H-Filtering
    Discrete-Time Certainty-Equivalent Filters (CEFs)
    Robust Discrete-Time Nonlinear H-Filtering

    Singular Nonlinear H-Control and H-Control for Singularly-Perturbed Nonlinear Systems
    Singular Nonlinear H-Control with State-Feedback
    Output Measurement-Feedback Singular Nonlinear H∞-Control
    Singular Nonlinear H-Control with Static Output-Feedback
    Singular Nonlinear H-Control for Cascaded Nonlinear Systems
    H-Control for Singularly-Perturbed Nonlinear Systems

    H-Filtering for Singularly-Perturbed Nonlinear Systems
    Problem Definition and Preliminaries
    Decomposition Filters
    Aggregate Filters
    Examples

    Mixed H2/H Nonlinear Control
    Continuous-Time Mixed H2/H Nonlinear Control
    Discrete-Time Mixed H2/H Nonlinear Control
    Extension to a General Class of Discrete-Time Nonlinear Systems

    Mixed H2/H Nonlinear Filtering
    Continuous-Time Mixed H2/HNonlinear Filtering
    Discrete-Time Mixed H2/H Nonlinear Filtering
    Example

    Solving the Hamilton-Jacobi Equation
    Review of Some Approaches for Solving the HJBE/HJIE
    Solving the Hamilton-Jacobi Equation for Mechanical Systems and Application to the Toda Lattice

    Biography

    M.D.S. Aliyu

    "This book is a comprehensive overview of nonlinear H-control theory for both continuous-time and discrete-time systems. ... The book can be used for a specialized or seminar course in robust and optimal control of nonlinear systems. It is written for practicing professionals, educators, researchers and graduate students in electrical, computer, mechanical, aeronautical, chemical, instrumentation, industrial and systems engineering, as well as applied mathematics, economics and management. I believe that this book will be cited in many future works in the field of H-control theory."
    —Vasile Drăgan (Bucharest), Mathematical Reviews, 2012D