Qualitative Abstraction of Piecewise Affine Systems
Michael Hofbaur · 2008
Qualitative or symbolic abstractions of hybrid systems re-ceived considerable interest recently to solve problems of hybrid systems estimation, control and verification symboli-cally. To abstract a hybrid system one has to slice the continu-ously valued input/output/state-space into a (finite) set of par-titions. The number of partitions potentially grows exponen-tially with the dimension of the space. As a consequence, one has to divide the spaces carefully in order to obtain a manage-able abstraction. This paper presents a systematic procedure to partition the state-space of piecewise affine (PWA) systems into qualitatively distinct regions. As a consequence, we ob-tain a moderately large set of partitions that characterises the hybrid dynamics of the PWA system. The abstraction scheme helps also to keep the number of so called spurious behaviors of qualitative simulation small, in particular when compared to the typically used grid-based abstractions.