Data-Driven Polytopic Approximation for an n-Dimensional Probabilistic Reachable Set

In this article, we first propose an algorithm to find a probabilistic reachable set (PRS) that bounds system states given a prescribed confidence level. Then, we establish an optimization framework using mixed integer linear programming, where the solution identifies a convex polytope that approximates the PRS. Utilizing this formulation, we have devised a heuristic algorithm aimed at efficiently determining its solution without compromising significant accuracy. Through case studies, we have tested this heuristic algorithm, showcasing its simultaneous benefits in terms of efficiency, accuracy, near-optimality, and robustness. The positive outcomes of this research lay the foundation for potential applications in the real-time, safety-critical motion planning of dynamic systems under uncertainties.