: Felix L. Chernous'ko, I. M. Ananievski, S. A. Reshmin
: Control of Nonlinear Dynamical Systems Methods and Applications
: Springer-Verlag
: 9783540707844
: 1
: CHF 132.70
:
: Maschinenbau, Fertigungstechnik
: English
: 396
: Wasserzeichen/DRM
: PC/MAC/eReader/Tablet
: PDF
This book is devoted to new methods of control for complex dynamical systems and deals with nonlinear control systems having several degrees of freedom, subjected to unknown disturbances, and containing uncertain parameters. Various constraints are imposed on control inputs and state variables or their combinations. The book contains an introduction to the theory of optimal control and the theory of stability of motion, and also a description of some known methods based on these theories. Major attention is given to new methods of control developed by the authors over the last 15 years. Mechanical and electromechanical systems described by nonlinear Lagrange's equations are considered. General methods are proposed for an effective construction of the required control, often in an explicit form. The book contains various techniques including the decomposition of nonlinear control systems with many degrees of freedom, piecewise linear feedback control based on Lyapunov's functions, methods which elaborate and extend the approaches of the conventional control theory, optimal control, differential games, and the theory of stability. The distinctive feature of the methods developed in the book is that the c- trols obtained satisfy the imposed constraints and steer the dynamical system to a prescribed terminal state in ?nite time. Explicit upper estimates for the time of the process are given. In all cases, the control algorithms and the estimates obtained are strictly proven.
Preface6
Contents8
Introduction13
Optimal control22
1.1 Statement of the optimal control problem22
1.2 The maximum principle27
1.3 Open-loop and feedback control32
1.4 Examples34
Method of decomposition (the first approach)41
2.1 Problem statement and game approach41
2.2 Control of the subsystem and feedback control design47
2.3 Weak coupling between degrees of freedom64
2.4 Nonlinear damping77
2.5 Applications and numerical examples92
Method of decomposition (the second approach)112
3.1 Problem statement and game approach112
3.2 Feedback control design and its generalizations121
3.3 Applications to robots140
Stability based control for Lagrangian mechanical systems155
4.1 Scleronomic and rheonomic mechanical systems155
4.2 Lyapunov stability of equilibrium159
4.3 Lyapunov’s direct method for autonomous systems159
4.4 Lyapunov’s direct method for nonautonomous systems161
4.5 Stabilization of mechanical systems161
4.6 Modification of Lyapunov’s direct method163
Piecewise linear control for mechanical systems under uncertainty164
5.1 Piecewise linear control for scleronomic systems164
5.2 Applications to mechanical systems177
5.3 Piecewise linear control for rheonomic systems206
Continuous feedback control for mechanical systems under uncertainty220
6.1 Feedback control for scleronomic system with a given matrix of inertia220
6.2 Control of a scleronomic system with an unknown matrix of inertia236
6.3 Control of rheonomic systems under uncertainty244
Control in distributed-parameter systems251
7.1 System of linear oscillators251
7.2 Distributed-parameter systems258
7.3 Solvability conditions269
Control system under complex constraints280
8.1 Control design in linear systems under complex constraints280
8.2 Application to oscillating systems286
8.3 Application to electro-mechanical systems308
Optimal control problems under complex constraints332
9.1 Time-optimal control problem under mixed and phase constraints333
9.2 Time-optimal control under constraints imposed on the rate of change of the acceleration345
9.3 Time-optimal control under constraints imposed on the acceleration and its rate of change359
Time-optimal swing-up and damping feedback controls of a nonlinear pendulum371
10.1 Optimal control structure372
10.2 Swing-up control376
10.3 Damping control384
References392
Index397