Approximating Reachable Sets of Linear Control System Using Multi-objective Programming

A continuous control system can be discretized into a discrete control system by numerical methods for ordinary differential equations. Studies have shown that the reachable set of a continuous control system can be approximated by its discrete counterpart. In this paper, utilizing the convex property of the reachable set of a linear control system, we propose a method to approximate the convex reachable set of a discrete linear control system with multi-objective programming (MOP). We treat the reachable set problem as solving multiple MOP problems and the convex hull of the non-dominated sets of these MOPs is the reachable set. For each MOP the revised normal boundary intersection method is used to obtain non-dominated points. Finally, we use computational experiments to clearly illustrate the validity of this method.