Control of Nonlinear Dynamical Systems

Methods and Applications

  • Felix L. Chernousko
  • Igor M. Ananievski
  • Sergey A. Reshmin

Part of the Communications and Control Engineering book series (CCE)

Table of contents

  1. Front Matter
    Pages I-9
  2. Felix L. Chernousko, Igor M. Ananievski, Sergey A. Reshmin
    Pages 11-29
  3. Felix L. Chernousko, Igor M. Ananievski, Sergey A. Reshmin
    Pages 31-101
  4. Felix L. Chernousko, Igor M. Ananievski, Sergey A. Reshmin
    Pages 103-145
  5. Felix L. Chernousko, Igor M. Ananievski, Sergey A. Reshmin
    Pages 147-155
  6. Felix L. Chernousko, Igor M. Ananievski, Sergey A. Reshmin
    Pages 157-212
  7. Felix L. Chernousko, Igor M. Ananievski, Sergey A. Reshmin
    Pages 213-243
  8. Felix L. Chernousko, Igor M. Ananievski, Sergey A. Reshmin
    Pages 245-273
  9. Felix L. Chernousko, Igor M. Ananievski, Sergey A. Reshmin
    Pages 275-326
  10. Felix L. Chernousko, Igor M. Ananievski, Sergey A. Reshmin
    Pages 327-365
  11. Felix L. Chernousko, Igor M. Ananievski, Sergey A. Reshmin
    Pages 367-387
  12. Back Matter
    Pages 389-396

About this book

Introduction

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, piece-wise 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 controls obtained satisfy the imposed constraints and steer the dynamical system to a prescribed terminal state in finite 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.

The methods are illustrated by a number of control problems for various engineering systems: robotic manipulators, pendular systems, electromechanical systems, electric motors, multibody systems with dry friction, etc. The efficiency of the proposed approaches is demonstrated by computer simulations. The authors hope that the monograph will be a useful contribution to the scientific literature on the theory and methods of control for dynamical systems. The book could be of interest for scientists and engineers in the field of applied mathematics, mechanics, theory of control and its applications, and also for students and postgraduates.

Keywords

algorithms control algorithm control theory dynamical system nonlinear control nonlinear control system optimal control stability system

Authors and affiliations

  • Felix L. Chernousko
    • 1
  • Igor M. Ananievski
    • 1
  • Sergey A. Reshmin
    • 1
  1. 1.Russian Academy of SciencesInstitute for Problems in MechanicsMoscowRussia 119526

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-540-70784-4
  • Copyright Information Springer-Verlag Berlin Heidelberg 2008
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Engineering
  • Print ISBN 978-3-540-70782-0
  • Online ISBN 978-3-540-70784-4
  • Series Print ISSN 0178-5354
  • About this book