Book description
A comprehensive overview of nonlinear H∞ control theory for both continuoustime and discretetime systems, Nonlinear H∞Control, Hamiltonian Systems and HamiltonJacobi Equations covers topics as diverse as singular nonlinear H∞control, nonlinear H∞ filtering, mixed H2/ H∞nonlinear control and filtering, nonlinear H∞almostdisturbancedecoupling,
and algorithms for solving the ubiquitous HamiltonJacobiIsaacs 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 HamiltonJacobi equation (HJE) has facilitated the application of HamiltonJacobi theory in both mechanics and control. As there is currently no efficient systematic analytical or numerical approach for solving them, the biggest bottleneck to the practical application of the nonlinear equivalent of the H∞control theory has been the difficulty in solving the HamiltonJacobiIsaacs partial differentialequations (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 HamiltonJacobi 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 ContinuousTime Nonlinear Systems
 3.2 H∞Gain Analysis for ContinuousTime Dissipative Systems
 3.3 ContinuousTime Passive Systems
 3.4 FeedbackEquivalence to a Passive ContinuousTime Nonlinear System
 3.5 Dissipativity and Passive Properties of DiscreteTime Nonlinear Systems
 3.6 ℓ2Gain Analysis for DiscreteTime Dissipative Systems
 3.7 FeedbackEquivalence to a DiscreteTime Lossless Nonlinear System
 3.8 Notes and Bibliography
 4 Hamiltonian Mechanics and HamiltonJacobi Theory

5 StateFeedback Nonlinear H∞Control for ContinuousTime Systems
 5.1 StateFeedback H∞Control for Affine Nonlinear Systems
 5.2 StateFeedback Nonlinear H∞ Tracking Control
 5.3 Robust Nonlinear H∞ StateFeedback Control
 5.4 StateFeedback H∞Control for TimeVarying Affine Nonlinear Systems
 5.5 StateFeedback H∞Control for StateDelayed Affine Nonlinear Systems
 5.6 StateFeedback H∞Control for a General Class of Nonlinear Systems
 5.7 Nonlinear H∞ AlmostDisturbanceDecoupling
 5.8 Notes and Bibliography

6 OutputFeedback Nonlinear H∞Control for ContinuousTime Systems
 6.1 Output MeasurementFeedback H∞Control for Affine Nonlinear Systems
 6.2 Output MeasurementFeedback Nonlinear H∞ Tracking Control
 6.3 Robust Output MeasurementFeedback Nonlinear H∞Control
 6.4 Output MeasurementFeedback H∞Control for a General Class of Nonlinear Systems
 6.5 Static OutputFeedback Control for Affine Nonlinear Systems
 6.6 Notes and Bibliography

7 DiscreteTime Nonlinear H∞Control
 7.1 FullInformation H∞Control for Affine Nonlinear DiscreteTime Systems
 7.2 Output MeasurementFeedback Nonlinear H∞Control for Affine DiscreteTime Systems
 7.3 Extensions to a General Class of DiscreteTime Nonlinear Systems
 7.4 Approximate Approach to the DiscreteTime Nonlinear H∞Control Problem
 7.5 Notes and Bibliography

8 Nonlinear H∞Filtering
 8.1 ContinuousTime Nonlinear H∞Filtering
 8.2 ContinuousTime Robust Nonlinear H∞Filtering
 8.3 CertaintyEquivalent Filters(CEFs)
 8.4 DiscreteTime Nonlinear H∞Filtering
 8.5 DiscreteTime CertaintyEquivalent Filters(CEFs)
 8.6 Robust DiscreteTime Nonlinear H∞Filtering
 8.7 Notes and Bibliography

9 Singular Nonlinear H∞Control and H∞Control for SingularlyPerturbed Nonlinear Systems
 9.1 Singular Nonlinear H∞Control with StateFeedback
 9.2 Output MeasurementFeedback Singular Nonlinear H∞Control
 9.3 Singular Nonlinear H∞Control with Static OutputFeedback
 9.4 Singular Nonlinear H∞Control for Cascaded Nonlinear Systems
 9.5 H∞Control for SingularlyPerturbed Nonlinear Systems
 9.6 Notes and Bibliography
 10 H∞Filtering for SingularlyPerturbed Nonlinear Systems
 11 Mixed H∞2/H∞∞ Nonlinear Control

12 Mixed H∞2/H∞∞ Nonlinear Filtering
 12.1 ContinuousTime Mixed H∞2/H∞∞ Nonlinear Filtering

12.2 DiscreteTime Mixed H∞2/H∞∞ Nonlinear Filtering
 12.2.1 Solution to the FiniteHorizon DiscreteTime Mixed H∞2/H∞∞ Nonlinear Filtering Problem
 12.2.2 Solution to the InfiniteHorizon DiscreteTime Mixed H∞2/H∞∞ Nonlinear Filtering Problem
 12.2.3 Approximate and Explicit Solution to the InfiniteHorizon DiscreteTime Mixed H∞2/H∞∞ Nonlinear Filtering Problem
 12.2.4 DiscreteTime CertaintyEquivalent Filters(CEFs)
 12.3 Example
 12.4 Notes and Bibliography
 13 Solving the HamiltonJacobi Equation
 A Proof of Theorem 5.7.1
 B Proof of Theorem 8.2.2
 Bibliography
 Index
Product information
 Title: Nonlinear HInfinity Control, Hamiltonian Systems and HamiltonJacobi Equations
 Author(s):
 Release date: December 2017
 Publisher(s): CRC Press
 ISBN: 9781351833219
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