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

ISBN-13: 9781439854839 / Angielski / Twarda / 2011 / 408 str.

M. D. S. Aliyu

Opis

A comprehensive overview of nonlinear H8 control theory for both continuous-time and discrete-time systems, Nonlinear H8-Control, Hamiltonian Systems and Hamilton-Jacobi Equations covers topics as diverse as singular nonlinear H8-control, nonlinear H8 -filtering, mixed H2/ H8-nonlinear control and filtering, nonlinear H8-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 H8-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.

Recenzje

"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

Spis treści

IntroductionHistorical Perspective on Nonlinear H∞-Control General Set-Up for Nonlinear H∞-Control Problems Notations and Preliminaries Basics of Differential GamesDynamic Programming PrincipleDiscrete-Time Nonzero-Sum Dynamic GamesContinuous-Time Nonzero-Sum Dynamic GamesTheory of Dissipative SystemsDissipativity of Continuous-Time Nonlinear Systems l2-Gain Analysis for Continuous-Time Dissipative Systems Continuous-Time Passive SystemsFeedback-Equivalence to a Passive Continuous-Time Nonlinear System Dissipativity and Passive Properties of Discrete-Time Nonlinear Systems l2-Gain Analysis for Discrete-Time Dissipative SystemsFeedback-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 LatticesThe Method of Characteristics for First-Order Partial-Differential EquationsLegendre Transform and Hopf-Lax FormulaState-Feedback Nonlinear H∞-Control for Continuous-Time SystemsState-Feedback H∞-Control for Affine Nonlinear SystemsState-Feedback Nonlinear H∞ Tracking ControlRobust Nonlinear H∞ State-Feedback ControlState-Feedback H∞-Control for Time-Varying Affine Nonlinear SystemsState-Feedback H∞-Control for State-Delayed Affine Nonlinear Systems State-Feedback H∞-Control for a General Class of Nonlinear SystemsNonlinear H∞ Almost-Disturbance-DecouplingOutput-Feedback Nonlinear H∞-Control for Continuous-Time SystemsOutput Measurement-Feedback H∞-Control for Affine Nonlinear Systems Output Measurement-Feedback Nonlinear H∞ Tracking ControlRobust 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 SystemsDiscrete-Time Nonlinear H∞-ControlFull-Information H∞-Control for Affine Nonlinear Discrete-Time SystemsOutput Measurement-Feedback Nonlinear H∞-Control for Affine Discrete-Time SystemsExtensions to a General Class of Discrete-Time Nonlinear SystemsApproximate Approach to the Discrete-Time Nonlinear H∞-Control ProblemNonlinear H∞-FilteringContinuous-Time Nonlinear H∞-Filtering Continuous-Time Robust Nonlinear H∞-FilteringCertainty-Equivalent Filters (CEFs)Discrete-Time Nonlinear H∞-FilteringDiscrete-Time Certainty-Equivalent Filters (CEFs)Robust Discrete-Time Nonlinear H∞-FilteringSingular Nonlinear H∞-Control and H∞-Control for Singularly-Perturbed Nonlinear SystemsSingular Nonlinear H∞-Control with State-FeedbackOutput Measurement-Feedback Singular Nonlinear H∞-ControlSingular Nonlinear H∞-Control with Static Output-FeedbackSingular Nonlinear H∞-Control for Cascaded Nonlinear SystemsH∞-Control for Singularly-Perturbed Nonlinear SystemsH∞-Filtering for Singularly-Perturbed Nonlinear SystemsProblem Definition and Preliminaries Decomposition Filters Aggregate Filters Examples Mixed H2/H∞ Nonlinear ControlContinuous-Time Mixed H2/H∞ Nonlinear Control Discrete-Time Mixed H2/H∞ Nonlinear Control Extension to a General Class of Discrete-Time Nonlinear SystemsMixed H2/H∞ Nonlinear FilteringContinuous-Time Mixed H2/H∞ Nonlinear FilteringDiscrete-Time Mixed H2/H∞ Nonlinear FilteringExampleSolving the Hamilton-Jacobi EquationReview of Some Approaches for Solving the HJBE/HJIE Solving the Hamilton-Jacobi Equation for Mechanical Systems and Application to the Toda Lattice

O autorze

M.D.S. Aliyu