Computational Advantages of a Two-level Hybrid Control Architecture

We investigate a two-level hierarchical architecture for hybrid control. On the top level, a discrete supervisory controller acts on quantised measurement information by switching between a finite number of continuous controllers in order to enforce a language inclusion specification. A widely accepted approach to this problem is to first construct a discrete abstraction of the continuous low-level feedback loops and to subsequently resort to DES techniques to solve the high-level synthesis problem. While in principle adopting this approach, we show how to use the structure induced by the low-level controllers to significantly increase computational efficiency of the abstraction procedure. Our methodology enables the system designer to exploit a trade-off between the increase in computational efficiency and the loss in controller flexibility caused by the specific hierarchical structure.