Computing observable and predictable subspaces to evaluate user-interfaces of LTI systems under shared control

We consider continuous-time LTI systems under shared control - that is, systems for which the continuous input is controlled by both a human operator and an automated-controller. The user-interface is a device through which the output of the system can be observed, and the control actions from the human can be entered. We identify observability-based conditions under which a user-interface provides the user with adequate information to accomplish a given task, formulated as a subset of the state-space. The “user-observable subspace” and the “user-predictable subspace” are calculated for two special cases: 1) when the user and the automation affect common control surfaces only, 2) when the user and the automation affect different control surfaces only. We apply our method to a real example of an aircraft accident during shared control.