Compositional Abstraction-Based Controller Synthesis for Continuous-Time Systems

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. It extends naturally to systems which are composed of weakly interconnected sub-components possibly connected in feedback, and models the coupling signals as disturbances. After proving this composability of disturbance bisimulation for metric systems we apply this result to the compositional abstraction of networks of input-to-state stable deterministic non-linear control systems. We give conditions that allow to construct finite-state abstractions compositionally for each component in such a network, so that the abstractions are simultaneously disturbance bisimilar to their continuous counterparts. Combining these two results, we show conditions under which one can compositionally abstract a network of non-linear control systems in a modular way while ensuring that the final composed abstraction is disturbance bisimilar to the original system. We discuss how we get a compositional abstraction-based controller synthesis methodology for networks of such systems against local temporal specifications as a by-product of our construction.