Compositional Synthesis of Finite-State Abstractions

Controller-synthesis techniques for continuous systems with respect to temporal logic specifications typically use a finite-state symbolic abstraction of the system model. Constructing this abstraction for the entire system is computationally expensive, and does not exploit natural decompositions of many systems into interacting components. We describe a methodology for compositional symbolic abstraction to help scale controller synthesis for temporal logic to larger systems. We introduce disturbance bisimulation, which strengthens the standard approximate alternating bisimulation relation used in control. It extends naturally to systems that are composed of weakly interconnected subcomponents, possibly connected in feedback, and models the coupling signals as disturbances. We show how networks of incrementally input-to-state stable, nonlinear, continuous-time control systems can be abstracted compositionally, so that all local abstractions are simultaneously disturbance bisimilar to their continuous counterparts. Furthermore, our construction ensures that the final composed abstraction is disturbance bisimilar to the original system. Finally, we discuss how we get a compositional abstraction-based controller-synthesis methodology for networks of such systems against local temporal specifications as a byproduct of our construction.