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

M.D.S. Aliyu

• Publisher: CRC Press
• Year: 2017
• ISBN:
  9781351833219
• Edition: 1
• Topic: Mathematics
• Subtopic: Applied Mathematics
• Index: Mathematics

A comprehensive overview of nonlinear H? control 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

• Cover
• Half Title
• Title Page
• Copyright Page
• Dedication
• Table of Contents
• 1 Introduction
• 2 Basics of Differential Games
• 3 Theory of Dissipative Systems
• 4 Hamiltonian Mechanics and Hamilton-Jacobi Theory
• 5 State-Feedback Nonlinear H∞-Control for Continuous-Time Systems
• 6 Output-Feedback Nonlinear H∞-Control for Continuous-Time Systems
• 7 Discrete-Time Nonlinear H∞-Control
• 8 Nonlinear H∞-Filtering
• 9 Singular Nonlinear H∞-Control and H∞-Control for Singularly-Perturbed Nonlinear Systems
• 10 H∞-Filtering for Singularly-Perturbed Nonlinear Systems
• 11 Mixed H∞2/H∞∞ Nonlinear Control
• 12 Mixed H∞2/H∞∞ Nonlinear Filtering
• 13 Solving the Hamilton-Jacobi Equation
• A Proof of Theorem 5.7.1
• B Proof of Theorem 8.2.2
• Bibliography
• Index