Aggregation Strategies in Reachable Set Computation of Hybrid Systems

Abstract

Computing the set of reachable states is a widely used technique for proving that a hybrid system satisfies its safety specification. Flow-pipe construction methods interleave phases of computing continuous successors and phases of computing discrete successors. Directly doing this leads to a combinatorial explosion problem, though, as with each discrete successor there may be an interval of time where the transition can occur, so that the number of paths becomes exponential in the number of discrete transitions. For this reason, most reachable set computation tools implement some form of set aggregation for discrete transitions, such as, performing a template-based overapproximation or convex hull aggregation. These aggregation methods, however, in theory can lead to unbounded error, and in practice are often the root cause of why a safety specification cannot be proven. This paper proposes techniques for improving the accuracy of the aggregation operations performed for reachable set computation. First, we present two aggregation strategies over generalized stars, namely convex hull aggregation and template based aggregation. Second, we perform adaptive deaggregation using a data structure called Aggregated Directed Acyclic Graph (AGGDAG). Our deaggregation strategy is driven by counterexamples and hence has soundness and relative completeness guarantees. We demonstrate the computational benefits of our approach through two case studies involving satellite rendezvous and gearbox meshing.