A Unified Safety Protection and Extension Governor

In this note, we propose a supervisory control scheme that unifies the abilities of safety protection and safety extension. It produces a control that keeps the system safe indefinitely when such a control exists. When such a control does not exist, it optimizes the control to maximize the time before any safety violation, which translates into more time to seek recovery and/or mitigate any harm. We describe the scheme and develop an approach that integrates the two abilities into a single constrained optimization problem with only continuous variables. For linear systems with convex constraints, the problem reduces to a convex quadratic program and is easy to solve. We illustrate the proposed safety supervisor with an automotive example.