Nonlinear and Optimal Control Theory

Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy June 19–29, 2004

  • Andrei A. Agrachev
  • A. Stephen Morse
  • Eduardo D. Sontag
  • Héctor J. Sussmann
  • Vadim I. Utkin
  • Paolo Nistri
  • Gianna Stefani

Part of the Lecture Notes in Mathematics book series (LNM, volume 1932)

Table of contents

About this book

Introduction

The lectures gathered in this volume present some of the different aspects of Mathematical Control Theory. Adopting the point of view of Geometric Control Theory and of Nonlinear Control Theory, the lectures focus on some aspects of the Optimization and Control of nonlinear, not necessarily smooth, dynamical systems. Specifically, three of the five lectures discuss respectively: logic-based switching control, sliding mode control and the input to the state stability paradigm for the control and stability of nonlinear systems. The remaining two lectures are devoted to Optimal Control: one investigates the connections between Optimal Control Theory, Dynamical Systems and Differential Geometry, while the second presents a very general version, in a non-smooth context, of the Pontryagin Maximum Principle. The arguments of the whole volume are self-contained and are directed to everyone working in Control Theory. They offer a sound presentation of the methods employed in the control and optimization of nonlinear dynamical systems.

Keywords

Nonlinear system Optimal control Pontryagin-Type differential equation differential geometry maximum maximum principle nonlinear control systems optimization

Authors and affiliations

  • Andrei A. Agrachev
    • 1
  • A. Stephen Morse
    • 2
  • Eduardo D. Sontag
    • 3
  • Héctor J. Sussmann
    • 3
  • Vadim I. Utkin
    • 4
  1. 1.SISSA-ISASInternational School for Advanced Studies34014Italy
  2. 2.Department of Electrical EngineeringYale UniversityNew HavenUSA
  3. 3.Department of Mathematics, Hill CenterRutgers UniversityPiscatawayUSA
  4. 4.Department of Electrical EngineeringThe Ohio State UniversityColumbusUSA

Editors and affiliations

  • Paolo Nistri
    • 1
  • Gianna Stefani
    • 2
  1. 1.Dipartimento di Ingegneria dell'InformazioneUniversità di SienaItaly
  2. 2.Dipartimento di Matematica Applicata “G. Sansone”Università di FirenzeItaly

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-540-77653-6
  • Copyright Information Springer Berlin Heidelberg 2008
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-540-77644-4
  • Online ISBN 978-3-540-77653-6
  • Series Print ISSN 0075-8434
  • About this book