hide
Free keywords:
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. Constructing this abstraction for the entire system is
computationally expensive, and does not exploit natural decompositions of many
systems into interacting components. We have recently introduced a new
relation, called (approximate) disturbance bisimulation for compositional
symbolic abstraction to help scale controller synthesis for temporal logic to
larger systems.
In this paper, we extend the results to stochastic control systems modeled by
stochastic differential equations. Given any stochastic control system
satisfying a stochastic version of the incremental input-to-state stability
property and a positive error bound, we show how to construct a finite-state
transition system (if there exists one) which is disturbance bisimilar to the
given stochastic control system. Given a network of stochastic control systems,
we give conditions on the simultaneous existence of disturbance bisimilar
abstractions to every component allowing for compositional abstraction of the
network system.
