Chernous'ko / Ananievski / Reshmin Control of Nonlinear Dynamical Systems

Methods and Applications
1. Auflage 2008
ISBN: 978-3-540-70784-4
Verlag: Springer Berlin Heidelberg
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 396 Seiten

Reihe: Communications and Control Engineering

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.

Autoren/Hrsg.

Chernous'ko, Felix L.

Ananievski, I. M.

Reshmin, S. A.

Inhaltsverzeichnis

1;Preface;6
2;Contents;8
3;Introduction;13
4;Optimal control;22
4.1;1.1 Statement of the optimal control problem;22
4.2;1.2 The maximum principle;27
4.3;1.3 Open-loop and feedback control;32
4.4;1.4 Examples;34
5;Method of decomposition (the first approach);41
5.1;2.1 Problem statement and game approach;41
5.2;2.2 Control of the subsystem and feedback control design;47
5.3;2.3 Weak coupling between degrees of freedom;64
5.4;2.4 Nonlinear damping;77
5.5;2.5 Applications and numerical examples;92
6;Method of decomposition (the second approach);112
6.1;3.1 Problem statement and game approach;112
6.2;3.2 Feedback control design and its generalizations;121
6.3;3.3 Applications to robots;140
7;Stability based control for Lagrangian mechanical systems;155
7.1;4.1 Scleronomic and rheonomic mechanical systems;155
7.2;4.2 Lyapunov stability of equilibrium;159
7.3;4.3 Lyapunov’s direct method for autonomous systems;159
7.4;4.4 Lyapunov’s direct method for nonautonomous systems;161
7.5;4.5 Stabilization of mechanical systems;161
7.6;4.6 Modification of Lyapunov’s direct method;163
8;Piecewise linear control for mechanical systems under uncertainty;164
8.1;5.1 Piecewise linear control for scleronomic systems;164
8.2;5.2 Applications to mechanical systems;177
8.3;5.3 Piecewise linear control for rheonomic systems;206
9;Continuous feedback control for mechanical systems under uncertainty;220
9.1;6.1 Feedback control for scleronomic system with a given matrix of inertia;220
9.2;6.2 Control of a scleronomic system with an unknown matrix of inertia;236
9.3;6.3 Control of rheonomic systems under uncertainty;244
10;Control in distributed-parameter systems;251
10.1;7.1 System of linear oscillators;251
10.2;7.2 Distributed-parameter systems;258
10.3;7.3 Solvability conditions;269
11;Control system under complex constraints;280
11.1;8.1 Control design in linear systems under complex constraints;280
11.2;8.2 Application to oscillating systems;286
11.3;8.3 Application to electro-mechanical systems;308
12;Optimal control problems under complex constraints;332
12.1;9.1 Time-optimal control problem under mixed and phase constraints;333
12.2;9.2 Time-optimal control under constraints imposed on the rate of change of the acceleration;345
12.3;9.3 Time-optimal control under constraints imposed on the acceleration and its rate of change;359
13;Time-optimal swing-up and damping feedback controls of a nonlinear pendulum;371
13.1;10.1 Optimal control structure;372
13.2;10.2 Swing-up control;376
13.3;10.3 Damping control;384
13.4;References;392
14;Index;397