Data-Driven Safe Control of Discrete-Time Non-Linear Systems

This letter proposes a framework to perform verifiably safe control of all discrete-time non-linear systems that are compatible with collected data. Most safety-maintaining control synthesis algorithms (e.g., control barrier functions, density functions) are limited to obtaining theoretical guarantees of safety in continuous-time, even while their implementation on real systems is typically in discrete-time. We first present a sum-of-squares based program to prove the existence of an (acausal) control policy that can safely stabilize all possible data-consistent systems. Causal control policies may be extracted by online optimization, and we provide sufficient conditions for the extraction of this control policy in general scenarios. As a specific case, we introduce a method for tractable online controller recovery when convexity assumptions are imposed on the candidate Lyapunov function and safety region descriptor. Discrete-time safe stabilization is demonstrated on three example systems.