Modern Control Engineering

Modern Control Engineering

Pergamon Unified Engineering Series

1st Edition - January 1, 1972

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  • Author: Maxwell Noton
  • eBook ISBN: 9781483186931

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Modern Control Engineering focuses on the methodologies, principles, approaches, and technologies employed in modern control engineering, including dynamic programming, boundary iterations, and linear state equations. The publication fist ponders on state representation of dynamical systems and finite dimensional optimization. Discussions focus on optimal control of dynamical discrete-time systems, parameterization of dynamical control problems, conjugate direction methods, convexity and sufficiency, linear state equations, transition matrix, and stability of discrete-time linear systems. The text then tackles infinite dimensional optimization, including computations with inequality constraints, gradient method in function space, quasilinearization, computation of optimal control-direct and indirect methods, and boundary iterations. The book takes a look at dynamic programming and introductory stochastic estimation and control. Topics include deterministic multivariable observers, stochastic feedback control, stochastic linear-quadratic control problem, general calculation of optimal control by dynamic programming, and results for linear multivariable digital control systems. The publication is a dependable reference material for engineers and researchers wanting to explore modern control engineering.

Table of Contents

  • Preface

    Chapter 1 State Representation of Dynamical Systems

    1.1 State Equations

    1.2 Linear State Equations

    1.3 Fundamental Matrices

    1.4 The Transition Matrix

    1.5 Inclusion of the Forcing or Control Variables

    1.6 Eigenvalues and Eigenvectors

    1.7 Discrete-Time State Equations

    1.8 Stability of Discrete-Time Linear Systems

    1.9 Controllability

    1.10 Observability


    Chapter 2 Finite Dimensional Optimization

    2.1 Motivation

    2.2 Unconstrained Maxima and Minima

    2.3 Equality Constraints

    2.4 Inequality Constraints

    2.5 Convexity and Sufficiency

    2.6 Linear Programming

    2.7 Direct Methods of Minimization

    2.8 An Illustrative Minimization Example

    2.9 Minimization by Steepest Descent

    2.10 Second Order Gradients

    2.11 Conjugate Direction Methods

    2.12 One Dimensional Searches

    2.13 Davidon-Fletcher-Powell

    2.14 Fletcher-Reeves

    2.15 Powell's Method

    2.16 Direct Methods for Constrained Minimization

    2.17 Penalty Functions

    2.18 Use of Transformations

    2.19 Parameterization of Dynamical Control Problems

    2.20 Optimal Control of Dynamical Discrete-Time Systems


    Chapter 3 Infinite Dimensional Optimization

    3.1 A Classic Problem and a Classical Solution

    3.2 Dynamical Optimization with no Terminal Constraints

    3.3 A Simple Control Problem

    3.4 Terminal Constraints and Variable Terminal Time

    3.5 An Elementary Thrust-Programming Problem

    3.6 A Foretaste of Computational Difficulties

    3.7 The Linear-Quadratic Control Problem

    3.8 Design of a Lateral Autostabilizer for an Aircraft

    3.9 Stability of the Linear-Quadratic Regulator

    3.10 Inequality Constraints

    3.11 Pontryagin's Maximum or Minimum Principle

    3.12 Additional Necessary Conditions and Sufficiency

    3.13 Singular Control

    3.14 Computation of Optimal Control — Direct and Indirect Methods

    3.15 Boundary Iterations

    3.16 Quasilinearization

    3.17 Gradient Method in Function Space

    3.18 Second Variations

    3.19 Conjugate Gradients

    3.20 Computations with Inequality Constraints


    Chapter 4 Dynamic Programming

    4.1 Historical Background

    4.2 A Multi-Stage Decision Problem

    4.3 The Principle of Optimality

    4.4 A Simple Control Problem in Discrete Time

    4.5 The General Calculation of Optimal Control by Dynamic Programming

    4.6 Results for Linear Multivariable Digital Control Systems

    4.7 An Example of Discrete-Time Control

    4.8 Computation of Nonlinear Discrete-Time Control

    4.9 The Continuous Form of Dynamic Programming

    4.10 A Special Solution of the Hamilton-Jacobi Equation

    4.11 Differential Dynamic Programming


    Chapter 5 Introductory Stochastic Estimation and Control

    5.1 Deterministic Multivariable Observers

    5.2 The Kaiman Filter

    5.3 Extensions of the Kaiman Filter

    5.4 An Example of the Extended Kaiman Filter

    5.5 Stochastic Feedback Control

    5.6 The Stochastic Linear-Quadratic Control Problem


    Chapter 6 Actual and Potential Applications

    6.1 Resume — Practical Significance of the Results

    6.2 Linear Control with Quadratic Criteria

    6.3 Static and Dynamic Optimization

    6.4 Applications of the Kaiman Filter

    Chapter 7 Appendices

    7.1 Stability of Discrete-Time Linear Systems

    7.2 Differentiation of Matrix Expressions

    7.3 Canonical Form for a Single-Output Linear System

    7.4 Markov Sequences

    Chapter 8 Supplement — Introduction to Matrices and State Variables

    8.1 Matrices and Vectors

    8.2 Numerical Solution of Ordinary Differential Equations

    8.3 The Generalized Newton-Raphson Process

    8.4 State Variable Characterization of Dynamical Systems

    Chapter 9 Bibliography and References


Product details

  • No. of pages: 288
  • Language: English
  • Copyright: © Pergamon 1972
  • Published: January 1, 1972
  • Imprint: Pergamon
  • eBook ISBN: 9781483186931

About the Author

Maxwell Noton

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