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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 a new relation, called (approximate) disturbance bisimulation, as the basis for compositional symbolic abstractions. Disturbance bisimulation strengthens the standard approximate alternating bisimulation relation used in control, and extends naturally to systems which are composed of sub-components possibly connected in feedback; disturbance bisimulation handles the feedback signals as disturbances. After proving this composability of disturbance bisimulation for metric systems, we show how one can construct finite-state abstractions compositionally for each component, so that the abstractions are simultaneously disturbance bisimilar to their continuous counterparts. Combining these two results, we can compositionally abstract a network system in a modular way while ensuring that the final composed abstraction is distrubance bisimilar to the original system. We discuss how we get a compositional controller synthesis methodology for networks of such systems against local temporal specifications as a by-product of our construction.

We present a lazy version of multi-layered abstraction-based controller synthesis (ABCS) for continuoustime nonlinear dynamical systems against safety specifications. State-of-the-art multi-layered ABCS uses pre-computed finitestate abstractions of different coarseness. Our new algorithm improves this technique by computing transitions on-the-fly, and only when a particular region of the state space needs to be explored by the controller synthesis algorithm for a specific coarseness. Additionally, our algorithm improves upon existing techniques by using coarser cells on a larger subset of the state space, which leads to significant computational savings.

Reactive synthesis and supervisory control theory both provide a design methodology for the automatic and algorithmic design of digital systems from declarative specifications. The reactive synthesis approach originates in computer science, and seeks to synthesise a system that interacts with its environment over time and that, doing so, satisfies a prescribed specification. Here, the distinguishing feature when compared to other synthesis problems in computer science is that the interaction is temporal in that it explicitly refers to a sequence of computation cycles. Supervisory control originates in control theory and seeks to synthesise a controller that-in closed-loop configuration with a plant-enforces a prescribed specification over time. The distinguishing feature compared to other branches of control is that all dynamics are driven by discrete events as opposed to continuous signals. While both methods apparently are closely related, the technical details differ significantly. We provide a formal comparison which allows us to identify conditions under which one can solve one synthesis problem using methods from the other one; we also discuss how the resulting solutions compare. To facilitate this comparison, we give a unified introduction to reactive synthesis and supervisory control and derive formal problem statements and a characterisation of their solutions in terms of ω-languages. Recent contributions to the two fields address different aspects of the respective problem, and we expect the formal relationship identified in this paper to be useful in that it allows the application of algorithmic techniques from one field in the other.

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