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 - 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