Reachability analysis for continuous systems under shared control: Application to user-interface design

We extend techniques for a reachability-based abstraction to continuous systems under shared control, that is, systems which have both inputs controlled by the automation and inputs controlled by the human, to account for potential interactions between the human and the automation that affect safety. We broadly classify human input as assisting the automated input, neutral, or fighting against the automated input, resulting in three types of invariance. Using standard reachability tools to calculate invariant, user-invariant, and user-assisted-invariant sets, regions in the state-space are associated with three levels of safety: (1) safe, (2) marginally safe, and (3) recoverably safe. By partitioning the state-space according to intersections of the invariant sets, we create an abstraction to a discrete event system of minimal cardinality which can inform the information content of a discrete user-interface that preserves information about the safety levels of the system. We apply the reachable set calculation and abstraction method to an aircraft landing under shared control.