Book description
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
- 3.1 Dissipativity of Continuous-Time Nonlinear 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
-
5 State-Feedback Nonlinear H∞-Control for Continuous-Time Systems
- 5.1 State-Feedback H∞-Control for Affine Nonlinear Systems
- 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
- 6.2 Output Measurement-Feedback Nonlinear H∞ Tracking Control
- 6.3 Robust Output Measurement-Feedback Nonlinear H∞-Control
- 6.4 Output Measurement-Feedback H∞-Control for a General Class of Nonlinear Systems
- 6.5 Static Output-Feedback Control for Affine Nonlinear Systems
- 6.6 Notes and Bibliography
-
7 Discrete-Time Nonlinear H∞-Control
- 7.1 Full-Information H∞-Control for Affine Nonlinear Discrete-Time Systems
- 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
- 7.4 Approximate Approach to the Discrete-Time Nonlinear H∞-Control Problem
- 7.5 Notes and Bibliography
-
8 Nonlinear H∞-Filtering
- 8.1 Continuous-Time Nonlinear H∞-Filtering
- 8.2 Continuous-Time Robust Nonlinear H∞-Filtering
- 8.3 Certainty-Equivalent Filters(CEFs)
- 8.4 Discrete-Time Nonlinear H∞-Filtering
- 8.5 Discrete-Time Certainty-Equivalent Filters(CEFs)
- 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
- 9.2 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
- 11 Mixed H∞2/H∞∞ Nonlinear Control
-
12 Mixed H∞2/H∞∞ Nonlinear Filtering
- 12.1 Continuous-Time Mixed H∞2/H∞∞ Nonlinear Filtering
-
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
- A Proof of Theorem 5.7.1
- B Proof of Theorem 8.2.2
- Bibliography
- Index
Product information
- Title: Nonlinear H-Infinity Control, Hamiltonian Systems and Hamilton-Jacobi Equations
- Author(s):
- Release date: December 2017
- Publisher(s): CRC Press
- ISBN: 9781351833219
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