## Abstract

The aim of this paper is to show how geometric techniques can solve optimization problems for two dimensional single-input control systems. We are first concerned with the problem of stabilization at the origin in minimum time, for a planar control system affine with respect to the control. A topological equivalence relation on the corresponding time-optimal feedback synthesis, was introduced in a previous paper. The set of equivalence classes can be put in a one to one correspondence with a discrete family of graphs. This provides a classification of the global structure of generic time-optimal stabilizing feedbacks in the plane, analogous to the classification of smooth dynamical systems developed by Peixoto. This analysis permit the study of many control systems encountered in the applications.

Original language | English (US) |
---|---|

Pages (from-to) | 1397-1402 |

Number of pages | 6 |

Journal | Proceedings of the IEEE Conference on Decision and Control |

Volume | 2 |

State | Published - Dec 1 1997 |

Event | Proceedings of the 1997 36th IEEE Conference on Decision and Control. Part 1 (of 5) - San Diego, CA, USA Duration: Dec 10 1997 → Dec 12 1997 |

## All Science Journal Classification (ASJC) codes

- Control and Systems Engineering
- Modeling and Simulation
- Control and Optimization