Realizable Set Invariance Conditions for Cyber-Physical Systems

There is currently a gap between control theoretical results and the reality of robotic implementations-this makes it difficult to transfer analytical guarantees to practice. This problem is especially troubling when it comes to safety guarantees for safety-critical systems. In this paper we seek to help bridge this gap. We first make a clear theoretical distinction between a system and a model, and outline how the two need to be related for guarantees to transfer from the latter to the former. We then introduce various imperfections into the model, including uncertainty in actuation and sensing, as well as time discretization effects from digital control implementations. These assumptions lead to new criteria for controlled invariance to be realizable. We investigate these criteria and propose a digital control implementation for enforcing safety in the presence of uncertainty. Our ideas are illustrated with a numerical example where a ground robot satisfies safety constraints in the presence of perception noise.