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Differential Geometry and Control
Edited by: G. Ferreyra, Louisiana State University, Baton Rouge, LA, R. Gardner, University of North Carolina, Chapel Hill, NC, H. Hermes, University of Colorado, Boulder, CO, and H. Sussmann, Rutgers University, New Brunswick, NJ

Proceedings of Symposia in Pure Mathematics
1999; 341 pp; hardcover
Volume: 64
ISBN-10: 0-8218-0887-7
ISBN-13: 978-0-8218-0887-0
List Price: US$96
Member Price: US$76.80
Order Code: PSPUM/64
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This volume presents selections from talks given at the AMS Summer Research Institute on Differential Geometry and Control held at the University of Colorado (Boulder). Included articles were refereed according to the highest standards. This collection provides a coherent global perspective on recent developments and important open problems in geometric control theory. Readers will find in this book an excellent source of current challenging research problems and results.


Graduate students, researchers, educators and applied mathematicians working in control theory; electrical, mechanical and aerospace engineers.

Table of Contents

  • G. R. Wilkens -- Remembering the mathematics of Robert Brown Gardner
  • A. Agrachev, G. Stefani, and P. Zezza -- A Hamiltonian approach to strong minima in optimal control
  • H. Airault -- The Heisenberg group \(H_3\) in terms of the orthonormal frame bundle \(O(R^2)\) and the control of variation of the Heisenberg diffusion
  • V. Ayala and J. Tirao -- Linear control systems on Lie groups and controllability
  • Z. Bartosiewicz -- Real analytic geometry and local observability
  • E. Pawłuszewicz and Z. Bartosiewicz -- External dynamic feedback equivalence of observable discrete-time control systems
  • R. M. Bianchini -- Good needle-like variations
  • A. M. Bloch and P. E. Crouch -- Representations of Dirac structures on vector spaces and nonlinear L-C circuits
  • B. Bonnard, M. Chyba, and I. Kupka -- Non integrable geodesics in SR-Martinet geometry
  • V. F. Borisov -- Singular extremals of order 3 and chattering
  • J.-M. Coron -- Some open problems in control theory
  • A. V. Dmitruk -- Quadratic order conditions of a local minimum for singular extremals in a general optimal control problem
  • T. E. Duncan -- Some solvable infinite time horizon stochastic control problems in hyperbolic three space
  • J. D. Lawson -- Geometric control and Lie semigroup theory
  • U. Ledzewicz and H. Schättler -- Analysis of abnormal extremals in optimal control
  • A. Marigo and A. Bicchi -- Rolling bodies with regular surface: The holonomic case
  • V. Ramakrishna -- On degenerate Monge-Ampere equations
  • F. Rampazzo -- Lie brackets and impulsive controls: An unavoidable connection
  • Y. L. Sachkov -- Survey on controllability of invariant systems on solvable Lie groups
  • G. R. Wilkens -- Centro-affine geometry in the plane and feedback invariants of two-state scalar control systems
  • J. Yang -- On hypersurfaces satisfying a basic equality
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