Stable Adaptive Control with Online Learning

Abstract

Learning algorithms have enjoyed numerous successes in robotic control tasks. In problems with time-varying dynamics, online learning methods have also proved to be a powerful tool for automatically tracking and/or adapting to the changing circumstances. However, for safety-critical ap- plications such as airplane flight, the adoption of these algorithms has been significantly hampered by their lack of safety, such as "stability," guarantees. Rather than trying to show difficult, a priori, stability guar- antees for specific learning methods, in this paper we propose a method for "monitoring" the controllers suggested by the learning algorithm on- line, and rejecting controllers leading to instability. We prove that even if an arbitrary online learning method is used with our algorithm to control a linear dynamical system, the resulting system is stable.