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

1. Auflage 2011
ISBN: 978-1-4398-5485-3
Verlag: CRC Press
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 408 Seiten

A comprehensive overview of nonlinear H8 control theory for both continuous-time and discrete-time systems, Nonlinear H8-Control, Hamiltonian Systems and Hamilton-Jacobi Equations covers topics as diverse as singular nonlinear H8-control, nonlinear H8 -filtering, mixed H2/ H8-nonlinear control and filtering, nonlinear H8-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 H8-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 H8-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.

Zielgruppe

Researchers and graduate students in control engineering, as well as researchers and graduate students in applied mathematics/ engineering mathematics.

Autoren/Hrsg.

Aliyu, M.D.S.

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik

Inhaltsverzeichnis

Introduction
Historical Perspective on Nonlinear H8-Control
General Set-Up for Nonlinear H8-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 H8-Control for Continuous-Time Systems
State-Feedback H8-Control for Affine Nonlinear Systems
State-Feedback Nonlinear H8 Tracking Control
Robust Nonlinear H8 State-Feedback Control
State-Feedback H8-Control for Time-Varying Affine Nonlinear Systems
State-Feedback H8-Control for State-Delayed Affine Nonlinear Systems
State-Feedback H8-Control for a General Class of Nonlinear Systems
Nonlinear H8 Almost-Disturbance-Decoupling

Output-Feedback Nonlinear H8-Control for Continuous-Time Systems
Output Measurement-Feedback H8-Control for Affine Nonlinear Systems
Output Measurement-Feedback Nonlinear H8 Tracking Control
Robust Output Measurement-Feedback Nonlinear H8-Control
Output Measurement-Feedback H8-Control for a General Class of Nonlinear Systems
Static Output-Feedback Control for Affine Nonlinear Systems

Discrete-Time Nonlinear H8-Control
Full-Information H8-Control for Affine Nonlinear Discrete-Time Systems
Output Measurement-Feedback Nonlinear H8-Control for Affine Discrete-Time Systems
Extensions to a General Class of Discrete-Time Nonlinear Systems
Approximate Approach to the Discrete-Time Nonlinear H8-Control Problem

Nonlinear H8-Filtering
Continuous-Time Nonlinear H8-Filtering
Continuous-Time Robust Nonlinear H8-Filtering
Certainty-Equivalent Filters (CEFs)
Discrete-Time Nonlinear H8-Filtering
Discrete-Time Certainty-Equivalent Filters (CEFs)
Robust Discrete-Time Nonlinear H8-Filtering

Singular Nonlinear H8-Control and H8-Control for Singularly-Perturbed Nonlinear Systems
Singular Nonlinear H8-Control with State-Feedback
Output Measurement-Feedback Singular Nonlinear H8-Control
Singular Nonlinear H8-Control with Static Output-Feedback
Singular Nonlinear H8-Control for Cascaded Nonlinear Systems
H8-Control for Singularly-Perturbed Nonlinear Systems

H8-Filtering for Singularly-Perturbed Nonlinear Systems
Problem Definition and Preliminaries
Decomposition Filters
Aggregate Filters
Examples

Mixed H2/H8 Nonlinear Control
Continuous-Time Mixed H2/H8 Nonlinear Control
Discrete-Time Mixed H2/H8 Nonlinear Control
Extension to a General Class of Discrete-Time Nonlinear Systems

Mixed H2/H8 Nonlinear Filtering
Continuous-Time Mixed H2/H8 Nonlinear Filtering
Discrete-Time Mixed H2/H8 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