| 中文摘要 | 第5-7页 |
| Abstract | 第7-8页 |
| 1 Introduction | 第12-18页 |
| 1.1 Background | 第12-15页 |
| 1.2 Motivation | 第15-16页 |
| 1.3 Dissertation outline | 第16-18页 |
| 2 Local control improvement for continuous systems | 第18-28页 |
| 2.1 General approach to approximate optimization | 第18-20页 |
| 2.2 Optimal control problem | 第20-22页 |
| 2.3 Control improvement algorithm | 第22-24页 |
| 2.4 Modifications | 第24-25页 |
| 2.5 Problems | 第25-28页 |
| 2.5.1 Problem 1 | 第25-27页 |
| 2.5.2 Problem 2 | 第27-28页 |
| 3 Local control improvement for discrete systems | 第28-39页 |
| 3.1 Problem formulation and preliminary results | 第28-30页 |
| 3.2 Control improvement | 第30-33页 |
| 3.2.1 Derivation of the improvement algorithm | 第30-31页 |
| 3.2.2 Iterative improvement algorithm | 第31-33页 |
| 3.3 Transformations to discrete-continuous systems | 第33-35页 |
| 3.4 Problems | 第35-39页 |
| 3.4.1 Problem 1 | 第35页 |
| 3.4.2 Problem 2. Parallel reaction problem | 第35-36页 |
| 3.4.3 Problem 3 | 第36-39页 |
| 4 Multistage approximate control optimization procedure | 第39-70页 |
| 4.1 Abstract optimization problem and principles of solving it | 第39-40页 |
| 4.2 General optimal control problem for a continuous system | 第40-48页 |
| 4.2.1 Constructing estimates for the boundaries of the admissible reachability set | 第45-48页 |
| 4.3 Transforming a controllable differential system in the general form to a system with linear controls | 第48-51页 |
| 4.3.1 Algorithm for convex hull construction | 第50-51页 |
| 4.4 General scheme for an approximate study of the original problem | 第51-52页 |
| 4.5 Problems | 第52-70页 |
| 4.5.1 Problem 1 | 第52-53页 |
| 4.5.2 Problem 2 | 第53-56页 |
| 4.5.3 Problem 3. Optimal control for a medical process | 第56-65页 |
| 4.5.4 Problem 4. Excitation transfer along a spin chain | 第65-70页 |
| 5 Global control improvement | 第70-91页 |
| 5.1 Abstract iterative optimization scheme | 第70-73页 |
| 5.2 Global control improvement for continuous systems | 第73-76页 |
| 5.3 Global control improvement for discrete systems | 第76-79页 |
| 5.4 Different implementations of global improvement methods | 第79-81页 |
| 5.5 Problems | 第81-91页 |
| 5.5.1 Problem 1. Controlling a linear oscillator | 第81-82页 |
| 5.5.2 Problem 2. Nonlinear nonconvex problem with special modes | 第82-83页 |
| 5.5.3 Problem 3. Classical nonconvex quadratic problem | 第83-84页 |
| 5.5.4 Problem 4. Case of a degenerate second variation of the functional | 第84-85页 |
| 5.5.5 Problem 5. Optimizing the control over treating a viral disease based on a simple model of the immune process | 第85-89页 |
| 5.5.6 Problem 6 | 第89-91页 |
| 6 Conclusions and expectations | 第91-94页 |
| Appendix | 第94-105页 |
| A1. The extension principle | 第94-98页 |
| A2. Derivative and limit systems | 第98-102页 |
| A3. Theorem 4.1 | 第102-105页 |
| References | 第105-114页 |
| Acknowledgements | 第114-115页 |
| Resume | 第115-119页 |
