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





ISBN 9781138072756
Published March 29, 2017 by CRC Press
405 Pages 30 B/W Illustrations

 
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Book Description

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.

Table of Contents

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

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Reviews

"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

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