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The theory of optimal control systems has grown and flourished since the 1960's. Many texts, written on varying levels of sophistication, have been published on the subject. Yet even those purportedly designed for beginners in the field are often riddled with complex theorems, and many treatments fail to include topics that are essential to a thorough grounding in the various aspects of and approaches to optimal control.
Optimal Control Systems provides a comprehensive but accessible treatment of the subject with just the right degree of mathematical rigor to be complete but practical. It provides a solid bridge between "traditional" optimization using the calculus of variations and what is called "modern" optimal control. It also treats both continuous-time and discrete-time optimal control systems, giving students a firm grasp on both methods. Among this book's most outstanding features is a summary table that accompanies each topic or problem and includes a statement of the problem with a step-by-step solution. Students will also gain valuable experience in using industry-standard MATLAB and SIMULINK software, including the Control System and Symbolic Math Toolboxes.
Diverse applications across fields from power engineering to medicine make a foundation in optimal control systems an essential part of an engineer's background. This clear, streamlined presentation is ideal for a graduate level course on control systems and as a quick reference for working engineers.
Table of Contents
INTRODUCTION
Classical and Modern Control
Optimization
Optimal Control
Historical Tour
About This Book
Chapter Overview
Problems
CALCULUS OF VARIATIONS AND OPTIMAL CONTROL
Basic Concepts
Optimum of a Function and a Functional
The Basic Variational Problem
The Second Variation
Extrema of Functions with Conditions
Extrema of Functionals with Conditions
Variational Approach to Optimal Systems
Summary of Variational Approach
Problems
LINEAR QUADRATIC OPTIMAL CONTROL SYSTEMS I
Problem Formulation
Finite-Time Linear Quadratic Regulator
Analytical Solution to the Matrix Differential Riccati Equation
Infinite-Time LQR System I
Infinite-Time LQR System II
Problems
LINEAR QUADRATIC OPTIMAL CONTROL SYSTEMS II
Linear Quadratic Tracking System: Finite-Time Case
LQT System: Infinite-Time Case
Fixed-End-Point Regulator System
Frequency-Domain Interpretation
Problems
DISCRETE-TIME OPTIMAL CONTROL SYSTEMS
Variational Calculus for Discrete-Time Systems
Discrete-Time Optimal Control Systems
Discrete-Time Linear State Regulator Systems
Steady-State Regulator System
Discrete-Time Linear Quadratic Tracking System
Frequency-Domain Interpretation
Problems
PONTRYAGIN MINIMUM PRINCIPLE
Constrained Systems
Pontryagin Minimum Principle
Dynamic Programming
The Hamilton-Jacobi-Bellman Equation
LQR System using H-J-B Equation
CONSTRAINED OPTIMAL CONTROL SYSTEMS
Constrained Optimal Control
TOC of a Double Integral System
Fuel-Optimal Control Systems
Minimum Fuel System: LTI System
Energy-Optimal Control Systems
Optimal Control Systems with State Constraints
Problems
APPENDICES
Vectors and Matrices
State Space Analysis
MATLAB Files
REFERENCES
INDEX
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Book Series
This book is included in the following series:
Electrical Engineering Series