Delay-incorporating observability and predictability analysis of safety-critical continuous-time systems

The authors suggest a framework for human-automation interaction in safety-critical continuous systems under shared control and consider continuous-time linear time-invariant (LTI) dynamics to formalise our physical models mathematically. Their goal is to determine whether or not a given user-interface provides the information required for a certain task, under the assumption that the user does not have access to any information beyond what is provided in the display. They identify observability-based conditions under which a user-interface provides the user with necessary information to accomplish a given task, formulated as a subset of the state space. They, therefore formulate the novel delay-incorporating user-observable subspace, and the delay-incorporating user-predictable subspace and compare them with the space spanned by the combination of the states which create the task. They assume the user is a special type of observer, with capabilities corresponding to different levels of knowledge regarding the current user´s input and its derivatives. In addition, they consider that state reconstruction and prediction incorporate a processing delay.