Advances in Control Systems
Theory and Applications
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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
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
Product details
- No. of pages: 334
- Language: English
- Copyright: © Academic Press 1966
- Published: January 1, 1966
- Imprint: Academic Press
- eBook ISBN: 9781483194622