Adversarially Robust Stability Certificates can be Sample-Efficient

Abstract

Motivated by bridging the simulation to reality gap in the context of safety-critical systems, we consider learning adversarially robust stability certificates for unknown nonlinear dynamical systems. In line with approaches from robust control, we consider additive and Lipschitz bounded adversaries that perturb the system dynamics. We show that under suitable assumptions of incremental stability on the underlying system, the statistical cost of learning an adversarial stability certificate is equivalent, up to constant factors, to that of learning a nominal stability certificate. Our results hinge on novel bounds for the Rademacher complexity of the resulting adversarial loss class, which may be of independent interest. To the best of our knowledge, this is the first characterization of sample-complexity bounds when performing adversarial learning over data generated by a dynamical system. We further provide a practical algorithm for approximating the adversarial training algorithm, and validate our findings on a damped pendulum example.

Online Adversarial Stabilization of Unknown Networked Systems

“…Therefore, the primary goal of control design is stabilization. Learning a stabilizing controller when the dynamics is unknown has been shown to be challenging even in the centralized case and many recent works focus on this sole issue, e.g., see Zhang et al (2021); Lamperski (2020); Perdomo et al (2021).…”