Robust stutter bisimulation for abstraction and controller synthesis with disturbance

This paper proposes a method to synthesise controllers for cyber-physical systems subjected to disturbances, such that the controlled system satisfies specifications given as linear temporal logic formulas. To solve this problem, a finite-state abstraction of the original system is first constructed, and then a controller is synthesised for the abstraction. Due to the disturbances and uncertainty in the environment, future states cannot be predicted exactly, and the abstraction must take this into account. For this purpose, the robust stutter bisimulation relation is introduced, which preserves the existence of controllers for any given linear temporal logic formula that excludes the next operator. States are related by the robust stutter bisimulation relation if the same target sets can be guaranteed to be reached or avoided under control of some controller, thus ensuring that disturbances have similar effect on paths that start in related states. It is shown that there exists a controller enforcing a linear temporal logic formula for the original system if and only if a controller exists for the abstracted system. The approach is illustrated by a robot navigation example. (c) 2023 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

Automated summary

This paper proposes a method to synthesise controllers for cyber-physical systems subjected to disturbances, such that the controlled system satisfies specifications given as linear temporal logic formulas. The approach constructs a finite-state abstraction of the original system and synthesises a controller for the abstraction. It introduces the robust stutter bisimulation relation to account for disturbances and uncertainty, ensuring that related states have similar effects under the same controller. The paper demonstrates that the existence of a controller for the abstracted system implies the existence of a controller for the original system enforcing the linear temporal logic formula.