Correct-By-Construction Exploration and Exploitation for Unknown Linear Systems Using Bilinear Optimization

This paper addresses the problem of controlling an unknown dynamical system to safely reach a target set. We assume we have a priori access to a finite set of uncertain linear systems, to which the unknown system belongs to. This set can contain models for different failure or operational modes or potential environmental conditions. Given a desired exploration-exploitation profile, we provide a bilinear optimization based solution to this control synthesis problem. Our approach provides a family of controllers that enable adaptation based on data observed at run-time to automatically trade off model detection and reachability objectives while maintaining safety. We demonstrate the approach with several examples.