Stabilization of Programmed Motion

Cover -- Half Title -- Title Page -- Copyright Page -- Table of Contents -- Introduction to the Series -- Preface -- Acknowledgements -- 0 Preliminaries -- 0.1 An Overview -- 0.1.1 Survey of Chapter 1 -- 0.1.2 Survey of Chapter 2 -- 0.1.3 Survey of Chapter 3 -- 0.1.4 Survey of Chapter 4 -- 1 Stabilization of Programmed Motions in General -- 1.0 Introduction -- 1.1 Statement of the Problems -- 1.1.1 Continuous stabilization problem -- 1.1.2 Linear stabilization problem -- 1.1.3 Relay stabilization problem -- 1.1.4 Stabilization problem with the choice of control directions -- 1.1.5 Stabilization problem with the use of auxiliary variables -- 1.2 Stabilization of Linear Stationary Systems -- 1.2.1 Systems with one control -- 1.2.2 Systems with several controls -- 1.2.3 Partially controlled systems -- 1.3 Stabilization of Linear Non- Stationary Systems -- 1.3.1 Systems with scalar control -- 1.3.2 Systems with several controls -- 1.3.3 Partially controlled systems -- 1.3.4 Some generalizations -- 1.4 System of Hierarchical Structure. Estimation of Inertia of Actuating and Measuring Devices -- 1.4.1 Systems of hierarchical structure with scalar control -- 1.4.2 Systems of hierarchical structure with vector control -- 1.4.3 Estimation of the inertia of measuring and actuating devices -- 1.5 Stabilization in a Strong Sense and Relay Stabilization -- 1.5.1 Stabilization in a strong sense -- 1.5.2 Relay stabilization -- 1.5.3 The structure of a limiting set appearing in relay stabilization -- 1.6 Stabilization of Systems with Coefficient Scattering -- 1.6.1 Linear non-stationary systems -- 1.6.2 Systems of hierarchical structure -- 1.7 Stabilization of Non-Stationary Systems with Incomplete Feedback -- 1.7.1 Lowering of the system order -- 1.7.2 Stabilization in a strong sense and relay stabilization

1.8 Stabilization with the Choice of Control Directions and the Use of Auxiliary Variables -- 1.8.1 Stabilization with the choice of control directions -- 1.8.2 Stabilization by means of auxiliary variables -- 1.9 Some Approaches to Controlled Uncertain Dynamic Systems -- 1.9.1 Stabilization problem -- 1.10 Comments and References -- 2 Stabilization in the Case of Discrete Information on the System State -- 2.0 Introduction -- 2.1 Formulation of Problems. Auxiliary Statements -- 2.1.1 Formulation of problems -- 2.1.2 Transition to difference equations -- 2.1.3 Auxiliary statements -- 2.2 Stabilization of Discrete Systems -- 2.2.1 Stabilization in the case of complete feedback -- 2.2.2 Stabilization in the case of incomplete feedback -- 2.3 Stabilization of Hybrid Systems -- 2.3.1 Linear stabilization of hybrid systems by means of controls of the form (2.1.4) -- 2.3.2 Linear stabilization of hybrid systems by means of controls of the form (2.1.5) -- 2.3.3 Linear stabilization of hybrid systems with the use of control directions and with the introduction of auxiliary variables -- 2.4 Comments and References -- 3 Optimal Control of Linear Equations and Quadratic Quality Criteria -- 3.0 Introduction -- 3.1 Statement of Main Problems -- 3.2 Optimal Stabilization of Non-Stationary Systems with Continuous Time -- 3.2.1 Systems with infinite functioning time -- 3.2.2 Systems with finite functioning time -- 3.3 Optimal Stabilization of Non-Stationary Systems with Discrete Time -- 3.3.1 Formulation and discussion of the results -- 3.3.2 Proof of Theorems 3.3.1-3.3.3 -- 3.4 Comments and References -- 4 Stabilization of Variable Structure Systems -- 4.0 Introduction -- 4.1 Statement of the Problems. Basic Results -- 4.1.1 Statement of the problems -- 4.1.2 Solution of orbital stability problem -- 4.1.3 Solution of orbital stabilization problem

4.2 Examples of Auto-Oscillation Construction -- 4.2.1 Auto-oscillation construction in systems with transistor switches -- 4.2.2 Auto-oscillation construction in systems with thyristor transformers -- 4.3 Comments and References -- References -- Subject Index