Advances in Control Systems

Theory and Applications

1st Edition, Volume 4 - January 1, 1966
Editor: C. T. Leondes
Language: English
eBook ISBN:
9 7 8 - 1 - 4 8 3 1 - 9 4 6 2 - 2

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… Read more

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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.

ContributorsPrefaceContents of Previous VolumesAlgorithms 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 ReferencesStability 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 ReferencesTrajectory Optimization Techniques I. Introduction II. Indirect Methods III. Method of Gradients IV. Second-Variation Method V. Generalized Newton-Raphson Method VI. Comparison of Methods ReferencesOptimum 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 ReferencesOptimal 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 ReferencesConvergence 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 ReferencesAuthor IndexSubject Index