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

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/H_∞ Nonlinear 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