Advances in Control Systems

Theory and Applications

1st Edition, Volume 5 - January 1, 1967
Editor: C. T. Leondes
Language: English
eBook ISBN:
9 7 8 - 1 - 4 8 3 1 - 9 4 6 6 - 0

Advances in Control Systems: Theory and Applications, Volume 5 provides information pertinent to the significant progress in the field of control and systems theory and… Read more

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Advances in Control Systems: Theory and Applications, Volume 5 provides information pertinent to the significant progress in the field of control and systems theory and applications. This book presents the problem of the optimal control of a system. Organized into six chapters, this volume begins with an overview of the fundamental conditions in the calculus of variations that are basic to the optimal control problem. This text then examines one of the basic problems in control and systems theory in general. Other chapters consider a number of rather basic results in optimal nonlinear filtering and describe the characteristic function of the state of vector of a nonlinear system. This book discusses as well a significant application area of control and systems theory, which is the optimal control of nuclear reactors. The final chapter deals with optimal control with bounds on the state variables. This book is a valuable resource for practicing engineers.

Contributors

Preface

Contents of Previous Volumes

Adaptive Optimal Steady State Control of Nonlinear Systems

I. Introduction

II. Formulation

III. Iterative Optimization

IV. Identification of the Performance Gradient

V. Multivariable Systems

References

An Initial Value Method for Trajectory Optimization Problems

I. Introduction

II. The Problem Statement

III. The Necessary Conditions and Reduced Differential Equations of the Extremals

IV. The Initial Value Problem and the Partial Derivatives

V. Computational Methods for Solving the Initial Value Problem

VI. Sufficiency Conditions

VII. Extensions of the Method

VIII. Examples

References

Determining Reachable Regions and Optimal Controls

I. Introduction to Optimal Control Problems and Reachable Regions

II. Carathéodory-Hamilton-Jacobi Approach in Optimal Control

III. A Heuristic Method of Determining the Reachable Region

IV. Rigorous Method of Determining the Reachable Region for a Particular Class of Problems

V. Illustration and Comparison of Rigorous and Heuristic Methods

VI. Concluding Remarks

References

Optimal Nonlinear Filtering

I. Introduction

II. The Dynamical Equation for Conditional Probability Density

III. Linear-Gaussian Case

IV. General Nonlinear, Non-Gaussian Case

V. Extensions and Applications of the Previous Results

VI. Examples

VII. Summary of Results and Areas for Future Research

Appendices

References

Optimal Control of Nuclear Reactor Systems

I. Introduction

II. The Reactor Kinetic State Equations

III. The Linearized State Equations

IV. Two Methods of Solution of the Linearized State Equation

V. Methods of Solution of the Kaplan Modes

VI. A Method of Estimating the Effects of Spatial Variation on Stability

VII. Analytical Design of a Spatial Feedback Control System

VIII. Examples

IX. Conclusions and Suggested Further Work

X. Appendices

List of Symbols

References

On Optimal Control with Bounded State Variables

I. Introduction

II. Necessary Conditions

III. Interpretation of the Necessary Conditions

IV. Computational Considerations

V. Summary and Conclusions

Appendix

References

Author Index

Subject Index