Advances in Control Systems, Volume 4

Contributors

Preface

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

References

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

References

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

References

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

References

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

References

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

References

Author Index

Subject Index

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.