Contents:Front Cover; Singular Optimal Control Problems; Copyright Page; CONTENTS; Preface; Chapter 1. An Historical Survey of Singular Control Problems; 1.1 Introduction; 1.2 Singular Control in Space Navigation; 1.3 Method of Miele via Green's Theorem; 1.4 Linear Systems - Quadratic Cost; 1.5 Necessary Conditions for Singular Optimal Control; 1.6 Sufficient Conditions and Necessary and Sufficient Conditions for Optimality; References; Chapter 2. Fundamental Concepts; 2.1 Introduction; 2.2 The General Optimal Control Problem; 2.3 The First Variation of J; 2.4 The Second Variation of J
2.5 A Singular Control ProblemReferences; Chapter 3. Necessary Conditions for Singularr Optimal Control; 3.1 Introduction; 3.2 The Generalized Legendre-Clebsch Condition; 3.3 Jacobson's Necessary Condition; References; Chapter 4. Sufficient Conditions and Necessary and Sufficient Conditions for Non-Negativity of Nonsingular and Singular Second Variations; 4.1 Introduction; 4.2 Preliminaries; 4.3 The Nonsingular Case; 4.4 Strong Positivity and the Totally Singular Second Variation; 4.5 A General Sufficiency Theorem for the Second Variation
4.6 Necessary and Sufficient Conditions for Non-negativity of the Totally Singular Second Variation4.7 Necessary Conditions for Optimality; 4.8 Other Necessary and Sufficient Conditions; 4.9 Sufficient Conditions for a Weak Local Minimum; 4.10 Existence Conditions for the Matrix Riccati Differential Equation; 4.11 Conclusion; References; Chapter 5. Computational Methods for Singular Control Problems; 5.1 Introduction; 5.2 Computational Application of the Sufficiency Conditions of Theorems 4.2 and 4.5; 5.3 Computation of Optimal Singular Controls
5.4 Joining of Optimal Singular and Nonsingular Sub-arcs5.5 Conclusion; References; Chapter 6. Conclusion; 6.1 The Importance of Singular Optimal Control Problems; 6.2 Necessary Conditions; 6.3 Necessary and Sufficient Conditions; 6.4 Computational Methods; 6.5 Switching Conditions; 6.6 Outlook for the Future; AUTHOR INDEX; SUBJECT INDEX