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cs.SY
Abstract:
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.
