Advances in Control Systems

Theory and Applications

1st Edition, Volume 1 - January 1, 1964
Editor: C. T. Leondes
Language: English
eBook ISBN:
9 7 8 - 1 - 4 8 3 1 - 9 4 6 5 - 3

Advances in Control Systems: Theory and Applications, Volume 1 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 1 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 the optimal method of controlling a given system with respect to the given criterion of performance. This text then summarizes some of the basic results of the maximum principle and illustrates how they may be exploited in control system studies. Other chapters consider the fundamental approach underlying almost all the existing works on the control of distributed parameter systems. This book discusses as well some important concepts in the theory of optimal control. The final chapter deals with the problem of controlling processes under the condition of uncertain changes in the process to be controlled. This book is a valuable resource for practicing engineers, applied mathematicians, and scientists.

Contributors

Preface

On Optimal and Suboptimal Policies in Control Systems

I. Introduction

II. Stochastic and Adaptive Control Systems

III. Approximate Realization of Desired Trajectories

IV. Existence of Optimal Controls

References

The Pontryagin Maximum Principle and Some of Its Applications

I. The Maximum Principle

II. Properties of Optimal Controls

III. An Application Study

References

Control of Distributed Parameter Systems

I. Introduction

II. System Description

III. Intrinsic Properties

IV. Optimum Control

V. Problems in Approximation and Computation

VI. Practical Aspects of Control

VII. Concluding Remarks

References

Optimal Control for Systems Described by Difference Equations

I. Introduction

II. Statement of the Problem

III. Set of Reachable Events and Huygens' Construction

IV. Principle of Optimal Evolution

V. A First Approach to the Maximum Principle

VI. Comoving Space Along a Trajectory

VII. Closure and Convexity of the Sets W(i) and W(i,V)

VIII. A General Proof of the Maximum Principle

IX. Existence Theorem

References

An Optimal Control Problem with State Vector Measurement Errors

I. Introduction and Preliminaries

II. Optimal Control in the Presence of State Vector Measurement Errors

III. Optimal Control in the Presence of Measurement Errors and Continuous Random Disturbances

IV. Optimal Control in the Presence of Measurement Errors and Random Disturbances Derived from the Generalized Poisson Process

V. Conclusions

VI. Appendices

References

On Line Computer Control Techniques and Their Application to Re-entry Aerospace Vehicle Control

I. Introduction

II. Optimum Linear Discrete Control

III. Synthesis of Control Forces with Inequality Constraints

IV. Identification of Process Parameters—Explicit Mathematical Relation Method

V. Identification of Process Parameters—Learning Model Method

VI. State Variable Estimation

VII. Application to the Re-entry Flight Control Problem

VIII. Summary and Suggested Extensions

Appendix 1. Notation and Concise Statement of Problems

Appendix 2. A Brute Force Method for the Quadratic Programming Problem

Appendix 3. Quadratic Programming Theorems

Appendix 4. A Recursive Method to Obtain the Best Estimate

Appendix 5. Correspondence Between Greville's and Kalman's Recursive Procedures

List of Symbols

References

Author Index

Subject Index