Computing Safe Sets of Linear Sampled-Data Systems

Leveraging autonomous systems in safety-critical applications requires formal robustness guarantees against uncertainties. We address this issue by computing safe terminal sets with corresponding safety-preserving terminal controllers, which ensure robust constraint satisfaction for an infinite time horizon. To maximize the region of operation, we also construct as large as possible safe initial sets that can be safely steered into the safe terminal set in finite time. We use scalable reachability analysis and convex optimization to efficiently compute safe sets of sampled-data systems. These systems are composed of a physical plant evolving in continuous time and a digital controller being implemented in discrete time. We further verify the effectiveness of our robust control approach using a simple double-integrator system and a vehicle-platooning benchmark.