Barrier-Based Test Synthesis for Safety-Critical Systems Subject to Timed Reach-Avoid Specifications

We propose an adversarial, time-varying test-synthesis procedure for safety-critical systems <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">without requiring specific knowledge of the underlying controller steering the system</i>. Specifically, our approach codifies the system objective as a timed reach-avoid specification. Then, by coupling control barrier functions with this class of specifications, we construct an instantaneous difficulty metric whose minimizer corresponds to the most difficult test at that system state. By defining tests as the minimizer of this difficulty metric over the space of allowable tests, we provably identify realizable and maximally difficult tests of system behavior. Finally, we develop this test-synthesis procedure for both continuous and discrete-time systems and showcase our test-synthesis procedure on simulated and hardware examples.