Nonlinear H-Infinity Control, Hamiltonian Systems and Hamilton-Jacobi Equations: 1st Edition (Paperback) book cover

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

1st Edition

By M.D.S. Aliyu

CRC Press

405 pages | 30 B/W Illus.

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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.

Reviews

"This book is a comprehensive overview of nonlinear H8-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 H8-control theory."

—Vasile Dragan (Bucharest), Mathematical Reviews, 2012D

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

Subject Categories

BISAC Subject Codes/Headings:
MAT003000
MATHEMATICS / Applied
TEC007000
TECHNOLOGY & ENGINEERING / Electrical