1st Edition

Optimal Control Systems

By D. Subbaram Naidu Copyright 2003
    460 Pages 111 B/W Illustrations
    by CRC Press

    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.

    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

    Biography

    D. Subbaram Naidu