Stability and Time-Optimal Control of Hereditary Systems

The following sections are included:

• Dedication

• Acknowledgment (First Edition)

• Acknowledgment (Second Edition)

• Contents

• Preface

• Preface to the Second Edition

The following sections are included:

• Ship Stabilization and Automatic Steering

• Predator-Prey Interactions

• Fluctuations of Current

• Control of Epidemics
  • First model
  • Control of epidemics: AIDS

• Wind Tunnel Model; Mach Number Control

• The Flip-Flop Circuit

• Hyperbolic Partial Differential Equations with Boundary Controls

• Control of Global Economic Growth

• The General Time-Optimal Control Problem and the Stability Problem
  • The stability problem

• Economic Models with Delay
  • Prices
  • Balance of payment
  • Employment and capital stock

• References

The following sections are included:

• The Fundamental Matrix of Retarded Equations
  • Using (2.1.10a) and (2.1.10b)
  • Using (2.1.8)

• The Variation of Constant Formula of Retarded Equations

• The Fundamental Solution of Linear Neutral Functional Differential Equations

• Linear Systems Stability [4]

• Examples

• Perturbed Linear Systems Stability

• References

The following sections are included:

• Lyapunov Stability Theory

• Razumikhin-Type Theorems

• Lyapunov–Razumikhin Methods of Stability in Delay Equations

• References

The following sections are included:

• Definitions

• Lyapunov Stability Theorem

• Perturbed Systems

• Perturbations of Nonlinear Neutral Systems

• References

The following sections are included:

• Control of Ordinary Linear Systems

• Synthesis of Time-Optimal Control of Linear Ordinary Systems

• Construction of Optimal Feedback Controls

• Time-Optimal Feedback Control of Nonautonomous Systems
  • The underdamped case (α² − ω² < 0)
  • Critically damped system (α² − ω² = 0)
  • Forming the switching curves
  • Terminal manifolds and switching locus

• Synthesis of Minimum-Effort Feedback Control Systems

• General Method for the Proof of Existence and Form of Time-Optimal, Minimum-Effort Control of Ordinary Linear Systems
  • Remarks on the assumptions

• References

The following sections are included:

• Euclidean Controllability of Linear Delay Systems

• Linear Function Space Controllability

• Constrained Controllability of Linear Delay Systems

• References

The following sections are included:

• Linear Systems in Euclidean Space

• Geometric Theory and Continuity of Minimal Time Function

• The Index of a Control System
  • Applications

• Time-Optimal Feedback Control of Autonomous Delay Systems

• Minimum-Effort Control of Delay Systems

• Proof of Minimum-Effort Theorems

• Optimal Absolute Fuel Function

• Control of Nonlinear Functional Differential Systems with Finite Delay: Existence, Uniqueness, and Continuity of Solutions

• Sufficient Conditions for the Existence of a Time-Optimal Control

• Optimal Control of Nonlinear Delay Systems with Target in Eⁿ

• Optimal Control of Delay Systems in Function Space

• The Time-Optimal Problem in Function Space

• References

The following sections are included:

• Controllability of Ordinary Nonlinear Systems

• Controllability of Nonlinear Delay Systems

• Controllability of Nonlinear Systems with Controls Appearing Linearly

• References

The following sections are included:

• Introduction

• Nonlinear Systems

• General Nonlinear Systems

• Examples

• Control of Global Economic Growth
  • Introduction
  • Preliminaries
  • Main results
  • Universal laws for the control of global economic growth

• Effective Solidarity Functions

• References

The following sections are included:

• The Time-Optimal Control Problem of Linear Neutral Functional Systems in Eⁿ: Introduction

• Forcing to Zero

• Normal and Proper Autonomous Systems

• Pursuit Gaines and Time-Optimal Control Theory

• Applications and Economic Growth

• Optimal Control Theory of Linear Neutral Systems

• The Theory of Time-Optimal Control of Linear Neutral Systems

• Existence Results

• Necessary Conditions for Optimal Control

• Normal Systems

• The Geometric Theory of Time-Optimal Control of Linear Neutral Systems

• Continuity of the Minimal-Time Functions

• The Index of the Control System

• Examples

• References

The following sections are included:

• Introduction

• Existence, Uniqueness, and Continuity of Solutions of Neutral Systems

• Existence of Optimal Controls of Neutral Systems

• Optimal Control of Neutral Systems in Function Space

• References

The following sections are included:

• Introduction

• General Nonlinear Systems

• Nonlinear Interconnected Systems

• An Example: A Network of Flip-Flop Circuits

• References

The following sections are included:

• Introduction

• Delay Systems

• Uniform Asymptotic Stability of Large-Scale Systems of Neutral Type

• General Comments

• References

The following sections are included:

• Appendix to Section 1.10

• Index