Reachability analysis of nonlinear analog circuits through iterative reachable set reduction

Abstract

We propose a methodology for reachability analysis of nonlinear analog circuits to verify safety properties. Our iterative reachable set reduction algorithm initially considers the entire state space as reachable. Our algorithm iteratively determines which regions in the state space are unreachable and removes those unreachable regions from the over approximated reachable set. We use the State Partitioning Tree (SPT) algorithm to recursively partition the reachable set into convex polytopes. We determine the reachability of adjacent neighbor polytopes by analyzing the direction of state space trajectories at the common faces between two adjacent polytopes. We model the direction of the trajectories as a reachability decision function that we solve using a sound root counting method. We are faithful to the nonlinearities of the system. We demonstrate the memory efficiency of our algorithm through computation of the reachable set of Van der Pol oscillation circuit.