A hierarchy of discrete abstractions for a hybrid plant
Jörg Raisch · Max Planck Institute for Plasma Physics · 1998
This contribution proposes a hierarchy of discrete abstractions for a given hybrid or continuous system with quantized measurements and symbolic control inputs. The continuous (or hybrid) base system and its discrete abstractions form a totally ordered set of models; ordering is in the sense of set inclusion of model behaviours or, equivalently, in terms of approximation accuracy. As, by construction, the behaviour of the base system is a subset of the behaviours of all abstractions in the hierarchy, any of these abstractions can be used for supervisory control synthesis: if a controller forces the behaviour of any abstraction to live within a specified set, it will also make the underlying continuous or hybrid system obey the specifications.