Computational Tools for the Safety Control of a Class of Piecewise Continuous Systems with Imperfect Information on a Partial Order

This paper addresses the two-agent safety control problem for piecewise continuous systemswith disturbances and imperfect state information. In particular, we focus on a class of systemsthat evolve on a partial order and whose dynamics preserve the ordering. While the safety con-trol problem with imperfect state information is prohibitive for general classes of nonlinear andhybrid systems, the class of systems considered in this paper admits an explicit solution. Wecompute this solution with linear complexity discrete-time algorithms that are guaranteed to ter-minate. The proposed algorithms are illustrated on a two-vehicle collision avoidance problem andimplemented on a hardware roundabout test-bed.