Advances in Control Systems

Theory and Applications

1st Edition, Volume 2 - January 1, 1965
Editor: C. T. Leondes
Language: English
eBook ISBN:
9 7 8 - 1 - 4 8 3 1 - 9 4 6 0 - 8

Advances in Control Systems: Theory and Applications, Volume 2 provides information pertinent to the significant progress in the field of automatic control. This book presents… Read more

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Advances in Control Systems: Theory and Applications, Volume 2 provides information pertinent to the significant progress in the field of automatic control. This book presents different methods for generating Liapunov functions, which is important in the analysis of nonlinear systems. Organized into five chapters, this volume begins with an overview of the reduction of the important method of Liapunov to a practical working tool for the analysis of complex nonlinear systems. This text then discusses applications of the rather powerful method of dynamic programming to a complex class of problems. Other chapters consider the mathematical theory of optimal control, which is often confronted with the task of solving a system of first-order ordinary differential equations. This book discusses as well the input–output relationship of multivariable linear systems or plants. The final chapter deals with a powerful technique for design by analysis of nonlinear systems. This book is a valuable resource for mathematicians and engineers.

Contributors

Preface

The Generation of Liapunov Functions

I. Introduction

II. Background, Definitions, and Theorems

III. Generation of Liapunov Functions for Autonomous Systems

IV. Generation of Liapunov Functions for Nonautonomous Systems

V. Conclusion

References

The Application of Dynamic Programming to Satellite Intercept and Rendezvous Problems

I. Introduction

II. The Optimal Control Problem

III. Optimal Estimation Problem

IV. Linearization Considerations

V. Computational Details

VI. Some Computational Results

List of Symbols

References

Synthesis of Adaptive Control Systems by Function Space Methods

I. Introduction

II. The Minimization Problem in Hilbert Space

III. Synthesis of Optimal Controls

IV. Final Value and Minimum Effort Systems

V. Least-Squares Estimation of Linear System Weighting Function Matrix

VI. Identification of Nonlinear Systems

VII. Optimal Control of Nonlinear Systems

VIII. Conclusions

References

Singular Solutions in Problems of Optimal Control

I. Introduction

II. Singular Solutions of Differential Equations

III. A Particular Class of Singular Solutions

IV. Some Preliminary Examples

V. Problems of Optimal Control

VI. A Summary of the Maximum Principle

VII. The Hamilton-Jacobi Equation

VIII. Problems of Optimal Control with the Control Appearing Linearly

IX. Singular Solutions in Problems of Optimal Control

X. The Singular Control Surface

XI. The Flooding Technique and Some Special Necessary Conditions for Optimal Singular Subarcs

XII. Allowable Switching Directions

XIII. The Singular Control

XIV. Singular Solutions and the Classical Calculus of Variations

XV. Singular Solutions in a More General Class of Optimal Control Problems

XVI. Examples

XVII. Appendix: Calculation of Expressions for the Singular Surface Ss

References

Several Applications of the Direct Method of Liapunov

Abstract

I. Introduction

II. A Sufficient Condition for the Stability of a Class of Systems

III. Applications of the Theorem of Linear Bounds

IV. Steepest-Descent Computation of the Inverse of a Singular Linear Function

References

Author Index

Subject Index