  Robust control is a core approach for controlling systems with performance
guarantees that are robust to modeling error, and is widely used in real-world
systems. However, current robust control approaches can only handle small
system uncertainty, and thus require significant effort in system
identification prior to controller design. We present an online approach that
robustly controls a nonlinear system under large model uncertainty. Our
approach is based on decomposing the problem into two sub-problems, "robust
control design" (which assumes small model uncertainty) and "chasing consistent
models", which can be solved using existing tools from control theory and
online learning, respectively. We provide a learning convergence analysis that
yields a finite mistake bound on the number of times performance requirements
are not met and can provide strong safety guarantees, by bounding the
worst-case state deviation. To the best of our knowledge, this is the first
approach for online robust control of nonlinear systems with such learning
theoretic and safety guarantees. We also show how to instantiate this framework
for general robotic systems, demonstrating the practicality of our approach.
