Safety controller synthesis for switched systems using multi-scale symbolic models

We propose a technique for the synthesis of safety controllers for switched systems using multi-scale abstractions. To this end we build on a recent notion of multi-scale discrete abstractions for incrementally stable switched systems. These abstractions are defined on a sequence of embedded lattices approximating the state-space, the finer ones being used only in a restricted area where fast switching is needed. This makes it possible to deal with fast switching while keeping the number of states in the abstraction at a reasonable level. We present a synthesis algorithm that exploits the specificities of multi-scale abstractions. The abstractions are computed on the fly during controller synthesis. The finest scales of the abstraction are effectively explored only when fast switching is needed, that is when the system approaches the unsafe set. We provide experimental results that show drastic improvements of the complexity of controller synthesis using multi-scale abstractions instead of uniform abstractions.