Optimal Control Theory An Introduction 1st edition by Donal Kirk ISBN 048632432X 978-0486434841

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ISBN 10: ‎ 048632432X
ISBN 13: 978-0486434841
Author: Donal Kirk

Optimal control theory is the science of maximizing the returns from and minimizing the costs of the operation of physical, social, and economic processes. Geared toward upper-level undergraduates, this text introduces three aspects of optimal control theory: dynamic programming, Pontryagin’s minimum principle, and numerical techniques for trajectory optimization.
Chapters 1 and 2 focus on describing systems and evaluating their performances. Chapter 3 deals with dynamic programming. The calculus of variations and Pontryagin’s minimum principle are the subjects of chapters 4 and 5, and chapter 6 examines iterative numerical techniques for finding optimal controls and trajectories. Numerous problems, intended to introduce additional topics as well as to illustrate basic concepts, appear throughout the text.

Optimal Control Theory: An Introduction 1st Table of contents:

1. Introduction to Optimal Control Theory

   • 1.1. What is Optimal Control?
   • 1.2. History and Development of Optimal Control
   • 1.3. Applications of Optimal Control
   • 1.4. Basic Principles of Control Systems
   • 1.5. Overview of the Mathematical Framework

2. Chapter 1: Mathematical Foundations

   • 2.1. Review of Calculus of Variations
   • 2.2. Differential Equations and Dynamic Systems
   • 2.3. Linear and Nonlinear Systems
   • 2.4. State-Space Representation
   • 2.5. Linear vs Nonlinear Control Systems

3. Chapter 2: The Optimal Control Problem

   • 3.1. Formulating the Optimal Control Problem
   • 3.2. Performance Criteria and Cost Functions
   • 3.3. Constraints in Optimal Control Problems
   • 3.4. Necessary Conditions for Optimality
   • 3.5. Control and State Variables

4. Chapter 3: The Pontryagin Maximum Principle

   • 4.1. Introduction to the Maximum Principle
   • 4.2. Derivation of the Pontryagin Maximum Principle
   • 4.3. Necessary Conditions for Optimality
   • 4.4. Hamiltonian Function and Its Properties
   • 4.5. Applications of the Maximum Principle

5. Chapter 4: The Hamilton-Jacobi-Bellman Equation

   • 5.1. Introduction to Dynamic Programming
   • 5.2. The Hamilton-Jacobi-Bellman (HJB) Equation
   • 5.3. Solving the HJB Equation
   • 5.4. Optimal Control in Linear Systems
   • 5.5. Applications of the HJB Equation in Optimal Control

6. Chapter 5: Linear Quadratic Regulator (LQR)

   • 6.1. The Linear Quadratic Problem
   • 6.2. The LQR Cost Function
   • 6.3. Solution to the LQR Problem
   • 6.4. State-Feedback Control Design
   • 6.5. Example Applications of LQR in Engineering

7. Chapter 6: Dynamic Programming and Bellman’s Principle

   • 7.1. Basic Principles of Dynamic Programming
   • 7.2. The Bellman Equation
   • 7.3. Optimal Control with Discrete Time Systems
   • 7.4. Applications of Dynamic Programming in Optimal Control
   • 7.5. Computational Techniques for Solving Optimal Control Problems

8. Chapter 7: Optimal Control for Linear Systems

   • 8.1. Linear State-Space Models
   • 8.2. Optimal Control with Linear Dynamics
   • 8.3. State and Output Feedback for Linear Systems
   • 8.4. Optimal Control with Disturbances
   • 8.5. Numerical Solution Methods for Linear Systems

9. Chapter 8: Nonlinear Optimal Control

   • 9.1. Nonlinear System Representation
   • 9.2. Optimal Control of Nonlinear Systems
   • 9.3. Approximation Methods for Nonlinear Systems
   • 9.4. Lyapunov’s Direct Method in Nonlinear Optimal Control
   • 9.5. Applications of Nonlinear Control

10. Chapter 9: Applications of Optimal Control

    • 10.1. Optimal Control in Robotics
    • 10.2. Optimal Control in Aerospace Systems
    • 10.3. Optimal Control in Automotive Systems
    • 10.4. Optimal Energy Management
    • 10.5. Environmental and Industrial Applications

11. Chapter 10: Computational Methods in Optimal Control

    • 11.1. Numerical Optimization Techniques
    • 11.2. Solving Optimal Control Problems with MATLAB
    • 11.3. Iterative Methods for Large-Scale Systems
    • 11.4. Stochastic Optimal Control
    • 11.5. Challenges in Computational Optimal Control

12. Appendices

    • A.1. Review of Linear Algebra
    • A.2. Solution Techniques for Ordinary Differential Equations
    • A.3. MATLAB Code for Optimal Control Problems
    • A.4. Glossary of Terms

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