Feedback control law generation for safety controller synthesis

In recent papers we have focused on the task of safety controller synthesis, that is, designing a controller that will take the system from any point within a compact set of initial states to a point inside a set of acceptable goal states, while never entering any state that is deemed unsafe. This method first finds a feedback controller that causes the system to be imbued with trajectory robustness, then finds open-loop reference signals that each safely drive the system from a subset of initial states to the goal state. In this paper we use piecewise affine system identification techniques to generate a feedback control law to replace the open-loop signals. This provides additional robustness to unexpected disturbances, in addition to reducing the memory required in the resulting controller, from storing many signals to a set of piecewise affine control laws.