Hierarchical Discrete Event Systems with Inputs and Outputs

We propose a framework for the hierarchical design of discrete event systems that addresses both safety and liveness properties. Technically, we build on a notion of inputs and outputs that is closely related to J.C. Willems´ behavioural systems theory. We develop a structural admissibility condition that allows for abstraction-based controller synthesis similar to previous work on hybrid control systems. A key feature of our framework is an alternation of subsystem composition and controller synthesis that is expected to be computationally efficient whenever the complexity of the safety specifications is independent of the respective layer in the hierarchy