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E-raamat: Stabilization of Programmed Motion [Taylor & Francis e-raamat]

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This monograph develops an optimal stabilization of programmed motion controlled systems. Smirnov (St. Petersburg State University) develops methods of constructing the stabilizing controls both continuous and discrete in level and time for controlled objects whose motions are described by both stationary and non-stationary systems of ordinary differential equations. The mobile objects are, for example, vessels, aircraft and artificial Earth satellites. When solving the stabilization problem, major attention is paid to the objects whose motion is described by differential equations with the right-hand part explicitly dependent on time and constructive parameters. For such systems, the methods which have nothing to do with the self-adjusting ideas are first developed to construct the controls stabilizing the controlled object motion without reference to a specific realization for the errors of its parameters. Annotation c. Book News, Inc., Portland, OR (booknews.com)

Presents a particular aspect of control theory-stabilization of programmed motion. Volume 14 in the Stability and Control Theory, Methods and Applications series.

This volume presents a particular aspect of control theory-stabilization of programmed motion. Methods of the construction and synthesis of stabilizing controls are introduced together with original results and useful examples. The problem of optimal stabilization control synthesis is solved for linear systems of difference equations with quadratic quality criterion.
Introduction to the Series ix
Preface xi
Acknowledgements xiii
Preliminaries
An Overview
1(2)
Survey of
Chapter 1
1(1)
Survey of
Chapter 2
2(1)
Survey of
Chapter 3
2(1)
Survey of
Chapter 4
3(1)
Basic Notions and Designations
3(6)
Stabilization of Programmed Motions in General
Introduction
9(1)
Statement of the Problems
9(6)
Continuous stabilization problem
10(1)
Linear stabilization problem
11(3)
Relay stabilization problem
14(1)
Stabilization problem with the choice of control directions
14(1)
Stabilization problem with the use of auxiliary variables
15(1)
Stabilization of Linear Stationary Systems
15(16)
Systems with one control
15(4)
Systems with several controls
19(10)
Partially controlled systems
29(2)
Stabilization of Linear Non-Stationary Systems
31(20)
Systems with scalar control
31(3)
Systems with several controls
34(8)
Partially controlled systems
42(2)
Some generalizations
44(7)
System of Hierarchical Structure. Estimation of Inertia of Actuating and Measuring Devices
51(21)
Systems of hierarchical structure with scalar control
51(12)
Systems of hierarchical structure with vector control
63(5)
Estimation of the inertia of measuring and actuating devices
68(4)
Stabilization in a Strong Sense and Relay Stabilization
72(18)
Stabilization in a strong sense
72(6)
Relay stabilization
78(5)
The structure of a limiting set appearing in relay stabilization
83(7)
Stabilization of Systems with Coefficient Scattering
90(12)
Linear non-stationary systems
90(7)
Systems of hierarchical structure
97(5)
Stabilization of Non-Stationary Systems with Incomplete Feedback
102(9)
Lowering of the system order
103(2)
Stabilization in a strong sense and relay stabilization
105(6)
Stabilization with the Choice of Control Directions and the Use of Auxiliary Variables
111(11)
Stabilization with the choice of control directions
111(3)
Stabilization by means of auxiliary variables
114(8)
Some Approaches to Controlled Uncertain Dynamic Systems
122(7)
Stabilization problem
122(7)
Comments and References
129(4)
Stabilization in the Case of Discrete Information on the System State
Introduction
133(1)
Formulation of Problems. Auxiliary Statements
133(14)
Formulation of Problems
133(2)
Transition to difference equations
135(5)
Auxiliary statements
140(7)
Stabilization of Discrete Systems
147(13)
Stabilization in the case of complete feedback
147(8)
Stabilization in the case of incomplete feedback
155(5)
Stabilization of Hybrid Systems
160(16)
Linear stabilization of hybrid systems by means of controls of the form (2.1.4)
160(7)
Linear stabilization of hybrid systems by means of controls of the form (2.1.5)
167(6)
Linear stabilization of hybrid systems with the use of control directions and with the introduction of auxiliary variables
173(3)
Comments and References
176(1)
Optimal Control of Linear Equations and Quadratic Quality Criteria
Introduction
177(1)
Statement of Main Problems
177(4)
Optimal Stabilization of Non-Stationary Systems with Continuous Time
181(17)
Systems with infinite functioning time
182(8)
Systems with finite functioning time
190(8)
Optimal Stabilization of Non-Stationary Systems with Discrete Time
198(14)
Formulation and discussion of the results
198(6)
Proof of Theorems 3.3.1-3.3.3
204(8)
Comments and References
212(3)
Stabilization of Variable Structure Systems
Introduction
215(1)
Statement of the Problems. Basic Results
215(19)
Statement of the problems
215(2)
Solution of orbital stability problem
217(11)
Solution of orbital stabilization problem
228(6)
Examples of Auto-Oscillation Construction
234(20)
Auto-oscillation construction in systems with transistor switches
234(6)
Auto-oscillation construction in systems with thyristor transformers
240(14)
Comments and References
254(3)
References 257(6)
Subject Index 263


E Ya Smirnov