Learning by doing: systematic abstraction refinement for hybrid control synthesis

Abstract

The synthesis of discrete event controllers for given continuous dynamics is studied within the hybrid system theory and its applications. A common approach involves the generation of a discrete abstraction of the continuous plant model, thus transforming the hybrid control problem into a purely discrete one that is then addressable using methods from the discrete event systems theory. In previous work, conditions were derived guaranteeing that successful synthesis on the abstraction level would provide a solution for the underlying hybrid problem. If synthesis failed, however, the abstraction was in need of refinement. This resulted in an iterative procedure alternating abstraction refinement with trial controller synthesis. The authors now use a temporal decomposition of the control problem to extract relevant diagnostic information when the synthesis step fails. In contrast with standard unfocused and global refinement strategies, the new iteration ‘learns by doing’ in the synthesis step and implements a refinement that is tailored to the particular hybrid plant and specification at hand.