Advances in Control Systems

Advances in Control Systems

Theory and Applications

1st Edition - January 1, 1966

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  • Editor: C. T. Leondes
  • eBook ISBN: 9781483194622

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Advances in Control Systems: Theory and Applications, Volume 4 provides information pertinent to the significant progress in the field of automatic control. This book presents several fundamental approaches to algorithms for the determination of optimum control inputs to a system. Organized into six chapters, this volume begins with an overview of presents the method of sequential optimization including examples of its application. This text then examines the powerful direct method of Liapunov function techniques to the subject of the stability of stochastic dynamical systems. Other chapters consider the aspect of optimum control of large-scale complex system, which is the most striking characteristic in the evolution of the practice of control systems theory. This book discusses as well the basic techniques for the modification of the control problem. The final chapter deals with the problem of convergence properties of the method of gradients. This book is a valuable resource for engineers.

Table of Contents

  • Contributors


    Contents of Previous Volumes

    Algorithms for Sequential Optimization of Control Systems

    I. Introduction

    II. Optimization of a Class of Linear Problems

    III. A Gradient Algorithm for the Linear Problem

    IV. Computational Aspects of the Linear Problem

    V. Numerical Experimentation with Linear Problems

    VI. Application to a Class of Nonlinear Problems

    VII. Summary and Conclusions

    Appendix. General Gradient Acceleration Method

    List of Symbols


    Stability of Stochastic Dynamical Systems

    I. Introduction

    II. Stochastic Liapunov Theorems

    III. Examples of the Stochastic Liapunov Theory

    IV. An Indirect Method for Linear Systems

    V. Application of Kronecker Products


    Trajectory Optimization Techniques

    I. Introduction

    II. Indirect Methods

    III. Method of Gradients

    IV. Second-Variation Method

    V. Generalized Newton-Raphson Method

    VI. Comparison of Methods


    Optimum Control of Multidimensional and Multilevel Systems

    I. Introduction

    II. Optimum Control of Linear Multidimensional Systems

    III. Optimum Distribution of Load by Second-Level Controller

    IV. Cyclic Optimization of Interacting Dynamic Subsystems

    V. Optimum Control of Aggregated Systems


    Optimal Control of Linear Stochastic Systems with Complexity Constraints

    I. Introduction

    II. Examples of Constrained-Optimal-Control Problems

    III. Formulation of the Constrained-Optimal-Control Problem

    IV. Solution of the Constrained-Optimal-Control Problem—Continuous Time

    V. Solution of the Constrained-Optimal-Control Problem—Discrete Time

    VI. Solution of Optimal-Control Problems in the Absence of Complexity Constraints

    VII. Numerical Results

    Appendix 1. Linearized Formulation of the Intercept Guidance Problem

    Appendix 2. Matrix Formulation of the Intercept Guidance Problem Using Proportional Navigation

    Appendix 3. Matrix Formulation of the Laning and Battin Problem

    Appendix 4. The Variance Equation

    Appendix 5. Solution for Singular Control Variables—Problems Nonlinear in the State

    Appendix 6. Numerical Solution of the Euler Equations in the Discrete Case

    Appendix 7. Convergence of the "Modified" Method of Local Optimization

    Appendix 8. Normalization of Control Gains

    Appendix 9. Convergence of the Gain Coefficients in Applications of Steepest Descent


    Convergence Properties of the Method of Gradients

    I. Summary and Definition of Problem

    II. Large-Amplitude Theory

    III. Small-Amplitude Theory

    IV. Discussion

    Appendix 1. Sensitivity of Peformance Index to Perturbations in Control in the Singular Case

    Appendix 2. Optimal Choice of Step Size and General Expression for Convergence of the Performance Index

    Appendix 3. Calculation of Rate of Convergence Versus Size of Smallest Eigenvalue

    Appendix 4. Calculation of Rate of Convergence Versus Structure of Spectrum Near Zero


    Author Index

    Subject Index

Product details

  • No. of pages: 334
  • Language: English
  • Copyright: © Academic Press 1966
  • Published: January 1, 1966
  • Imprint: Academic Press
  • eBook ISBN: 9781483194622

About the Editor

C. T. Leondes

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