Null-controllable set computation for a class of constrained bilinear systems

We present a method for the exact computation of null-controllable sets for single-input bilinear systems with input and state constraints. The proposed approach is based on first linearizing the bilinear system exactly, and applying known methods for the recursive calculation of null-controllable sets subsequently. While these steps are obvious from a conceptual point of view, it has to be taken into account that the constraints are transformed in the exact linearization step. Unfortunately, the transformed constraints are in general non-convex, even if the original constraints are convex. We show how to represent the transformed constraints in terms of a finite number of convex sets, which is instrumental for the computer-based evaluation of the null-controllable sets.