Home Page Icon
Home Page
Table of Contents for
Cover
Close
Cover
by M.D.S. Aliyu
Nonlinear H-Infinity Control, Hamiltonian Systems and Hamilton-Jacobi Equations
Cover
Half Title
Title Page
Copyright Page
Dedication
Table of Contents
1 Introduction
1.1 Historical Perspective on Nonlinear H∞-Control
1.2 General Set-Up for Nonlinear H∞-Control Problems
1.2.1 Mixed H2-Control Problem
1.2.2 Robust H∞-Control Problem
1.2.3 Nonlinear H∞-Filtering
1.2.4 Organization of the Book
1.3 Notations and Preliminaries
1.3.1 Notation
1.3.2 Stability Concepts
1.4 Notes and Bibliography
2 Basics of Differential Games
2.1 Dynamic Programming Principle
2.2 Discrete-Time Nonzero-Sum Dynamic Games
2.2.1 Linear-Quadratic Discrete-Time Dynamic Games
2.3 Continuous-Time Nonzero-Sum Dynamic Games
2.3.1 Linear-Quadratic Continuous-Time Dynamic Games
2.4 Notes and Bibliography
3 Theory of Dissipative Systems
3.1 Dissipativity of Continuous-Time Nonlinear Systems
3.1.1 Stability of Continuous-Time Dissipative Systems
3.1.2 Stability of Continuous-Time Dissipative Feedback-Systems
3.2 H∞-Gain Analysis for Continuous-Time Dissipative Systems
3.3 Continuous-Time Passive Systems
3.4 Feedback-Equivalence to a Passive Continuous-Time Nonlinear System
3.5 Dissipativity and Passive Properties of Discrete-Time Nonlinear Systems
3.6 ℓ2-Gain Analysis for Discrete-Time Dissipative Systems
3.7 Feedback-Equivalence to a Discrete-Time Lossless Nonlinear System
3.8 Notes and Bibliography
4 Hamiltonian Mechanics and Hamilton-Jacobi Theory
4.1 The Hamiltonian Formulation of Mechanics
4.2 Canonical Transformation
4.2.1 The Transformation Generating Function
4.2.2 The Hamilton-Jacobi Equation (HJE)
4.2.3 Time-Independent Hamilton-Jacobi Equation and Separation of Variables
4.3 The Theory of Nonlinear Lattices
4.3.1 The G2 Periodic Toda Lattice
4.4 The Method of Characteristics for First-Order Partial-Differential Equations
4.4.1 Characteristics for Quasi-Linear Equations
4.4.2 Characteristics for the General First-Order Equation
4.4.3 Characteristics for the Hamilton-Jacobi Equation
4.5 Legendre Transform and Hopf-Lax Formula
4.5.1 Viscosity Solutions of the HJE
4.6 Notes and Bibliography
5 State-Feedback Nonlinear H∞-Control for Continuous-Time Systems
5.1 State-Feedback H∞-Control for Affine Nonlinear Systems
5.1.1 Dissipative Analysis
5.1.2 Controller Parametrization
5.2 State-Feedback Nonlinear H∞ Tracking Control
5.3 Robust Nonlinear H∞ State-Feedback Control
5.4 State-Feedback H∞-Control for Time-Varying Affine Nonlinear Systems
5.5 State-Feedback H∞-Control for State-Delayed Affine Nonlinear Systems
5.6 State-Feedback H∞-Control for a General Class of Nonlinear Systems
5.7 Nonlinear H∞ Almost-Disturbance-Decoupling
5.8 Notes and Bibliography
6 Output-Feedback Nonlinear H∞-Control for Continuous-Time Systems
6.1 Output Measurement-Feedback H∞-Control for Affine Nonlinear Systems
6.1.1 Controller Parameterization
6.2 Output Measurement-Feedback Nonlinear H∞ Tracking Control
6.3 Robust Output Measurement-Feedback Nonlinear H∞-Control
6.3.1 Reliable Robust Output-Feedback Nonlinear H∞-Control
6.4 Output Measurement-Feedback H∞-Control for a General Class of Nonlinear Systems
6.4.1 Controller Parametrization
6.5 Static Output-Feedback Control for Affine Nonlinear Systems
6.5.1 Static Output-Feedback Control with Disturbance-Attenuation
6.6 Notes and Bibliography
7 Discrete-Time Nonlinear H∞-Control
7.1 Full-Information H∞-Control for Affine Nonlinear Discrete-Time Systems
7.1.1 State-Feedback H∞-Control for Affine Nonlinear Discrete-Time Systems
7.1.2 Controller Parametrization
7.2 Output Measurement-Feedback Nonlinear H∞-Control for Affine Discrete-Time Systems
7.3 Extensions to a General Class of Discrete-Time Nonlinear Systems
7.3.1 Full-Information H∞-Control for a General Class of Discrete-Time Nonlinear Systems
7.3.2 Output Measurement-Feedback H∞-Control for a General Class of Discrete-Time Nonlinear Systems
7.4 Approximate Approach to the Discrete-Time Nonlinear H∞-Control Problem
7.4.1 An Approximate Approach to the Discrete-Time State-Feedback Problem
7.4.2 An Approximate Approach to the Discrete-Time Output Measurement-Feedback Problem
7.5 Notes and Bibliography
8 Nonlinear H∞-Filtering
8.1 Continuous-Time Nonlinear H∞-Filtering
8.1.1 Infinite-Horizon Continuous-Time Nonlinear H∞-Filtering
8.1.2 The Linearized Filter
8.2 Continuous-Time Robust Nonlinear H∞-Filtering
8.3 Certainty-Equivalent Filters(CEFs)
8.3.1 2-DOFCertainty-Equivalent Filters
8.4 Discrete-Time Nonlinear H∞-Filtering
8.4.1 Infinite-Horizon Discrete-Time Nonlinear H∞-Filtering
8.4.2 Approximate and Explicit Solution
8.5 Discrete-Time Certainty-Equivalent Filters(CEFs)
8.5.1 2-DOF Proportional-Derivative (PD) CEFs
8.5.2 Approximate and Explicit Solution
8.6 Robust Discrete-Time Nonlinear H∞-Filtering
8.7 Notes and Bibliography
9 Singular Nonlinear H∞-Control and H∞-Control for Singularly-Perturbed Nonlinear Systems
9.1 Singular Nonlinear H∞-Control with State-Feedback
9.1.1 State-Feedback Singular Nonlinear H∞-Control Using High-Gain Feedback
9.2 Output Measurement-Feedback Singular Nonlinear H∞-Control
9.3 Singular Nonlinear H∞-Control with Static Output-Feedback
9.4 Singular Nonlinear H∞-Control for Cascaded Nonlinear Systems
9.5 H∞-Control for Singularly-Perturbed Nonlinear Systems
9.6 Notes and Bibliography
10 H∞-Filtering for Singularly-Perturbed Nonlinear Systems
10.1 Problem Definition and Preliminaries
10.2 Decomposition Filters
10.3 Aggregate Filters
10.4 Examples
10.5 Notes and Bibliography
11 Mixed H∞2/H∞∞ Nonlinear Control
11.1 Continuous-Time Mixed H∞2/H∞∞ Nonlinear Control
11.1.1 The Infinite-Horizon Problem
11.1.2 Extension to a General Class of Nonlinear Systems
11.2 Discrete-Time Mixed H∞2/H∞∞ Nonlinear Control
11.2.1 The Infinite-Horizon Problem
11.3 Extension to a General Class of Discrete-Time Nonlinear Systems
11.4 Notes and Bibliography
12 Mixed H∞2/H∞∞ Nonlinear Filtering
12.1 Continuous-Time Mixed H∞2/H∞∞ Nonlinear Filtering
12.1.1 Solution to the Finite-Horizon Mixed H∞2/H∞∞ Nonlinear Filtering Problem
12.1.2 Solution to the Infinite-Horizon Mixed H∞2/H∞∞ Nonlinear Filtering
12.1.3 Certainty-Equivalent Filters(CEFs)
12.2 Discrete-Time Mixed H∞2/H∞∞ Nonlinear Filtering
12.2.1 Solution to the Finite-Horizon Discrete-Time Mixed H∞2/H∞∞ Nonlinear Filtering Problem
12.2.2 Solution to the Infinite-Horizon Discrete-Time Mixed H∞2/H∞∞ Non-linear Filtering Problem
12.2.3 Approximate and Explicit Solution to the Infinite-Horizon Discrete-Time Mixed H∞2/H∞∞ Nonlinear Filtering Problem
12.2.4 Discrete-Time Certainty-Equivalent Filters(CEFs)
12.3 Example
12.4 Notes and Bibliography
13 Solving the Hamilton-Jacobi Equation
13.1 Review of Some Approaches for Solving the HJBE/HJIE
13.1.1 Solving the HJIE/HJBE Using Polynomial Expansion and Basis Functions
13.2 A Factorization Approach for Solving the HJIE
13.2.1 Worked Examples
13.3 Solving the Hamilton-Jacobi Equation for Mechanical Systems and Application to the Toda Lattice
13.3.1 Solving the Hamilton-Jacobi Equation
13.3.2 Solving the Hamilton-Jacobi Equation for the A2-Toda System
13.4 Notes and Bibliography
A Proof of Theorem 5.7.1
B Proof of Theorem 8.2.2
Bibliography
Index
Search in book...
Toggle Font Controls
Playlists
Add To
Create new playlist
Name your new playlist
Playlist description (optional)
Cancel
Create playlist
Sign In
Email address
Password
Forgot Password?
Create account
Login
or
Continue with Facebook
Continue with Google
Sign Up
Full Name
Email address
Confirm Email Address
Password
Login
Create account
or
Continue with Facebook
Continue with Google
Next
Next Chapter
Half Title
Add Highlight
No Comment
..................Content has been hidden....................
You can't read the all page of ebook, please click
here
login for view all page.
Day Mode
Cloud Mode
Night Mode
Reset