**Proceedings of Symposia in Pure Mathematics**

Volume: 64;
1999;
341 pp;
Hardcover

MSC: Primary 49; 53; 93;
Secondary 22; 60; 35

Print ISBN: 978-0-8218-0887-0

Product Code: PSPUM/64

List Price: $101.00

Individual Member Price: $80.80

**Electronic ISBN: 978-0-8218-9368-5
Product Code: PSPUM/64.E**

List Price: $101.00

Individual Member Price: $80.80

# Differential Geometry and Control

Share this page *Edited by *
*G. Ferreyra; R. Gardner; H. Hermes; H. Sussmann*

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.

#### Readership

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

# Table of Contents

## Differential Geometry and Control

- Contents v6 free
- Preface vii8 free
- Remembering the mathematics of Robert Brown Gardner 110 free
- A Hamiltonian approach to strong minima in optimal control 1120
- The Heisenberg group H[sub(3)] in terms of the orthonormal frame bundle 0(R[sup(2)]) and the control of variation of the Heisenberg diffusion 2332
- Linear control systems on Lie groups and controllability 4756
- Real analytic geometry and local observability 6574
- External dynamic feedback equivalence of observable discrete-time control systems 7382
- Good needle-like variations 91100
- Representations of Dirac structures on vector spaces and nonlinear L-C circuits 103112
- Non integrable geodesies in SR-Martinet geometry 119128
- Singular extremals of order 3 and chattering 135144
- Some open problems in control theory 149158
- Quadratic order conditions of a local minimum for singular extremals in a general optimal control problem 163172
- Some solvable infinite time horizon stochastic control problems in hyperbolic three space 199208
- Geometric control and Lie semigroup theory 207216
- Analysis of abnormal extremals in optimal control 223232
- Rolling bodies with regular surface: The holonomic case 241250
- On degenerate Monge-Ampere equations 257266
- Lie brackets and impulsive controls: An unavoidable connection 279288
- Survey on controllability of invariant systems on solvable Lie groups 297306
- Centro-affine geometry in the plane and feedback invariants of two-state scalar control systems 319328
- On hypersurfaces satisfying a basic equality 335344