On-the-fly, data-driven reachability analysis and control of unknown systems: an F-16 aircraft case study

We describe data-driven algorithms, DaTaReach and DaTaControl, for reachability analysis and control of systems with a priori unknown nonlinear dynamics. The resulting algorithms provide provable performance guarantees while satisfying real-time constraints. To this end, they merge data from a single finite-horizon trajectory and, if available, various forms of side information derived from laws of physics and qualitative properties of the system. Specifically, DaTaReach constructs a differential inclusion that contains the unknown vector field. Then, it over-approximates the reachable set through interval Taylor-based methods applied to systems with dynamics described as differential inclusions. DaTaControl achieves near-optimal and convex-optimization-based control of the system through the computed over-approximations and the receding horizon framework. We empirically demonstrate that DaTaControl outperforms, in terms of optimality of the control and computation time, state-of-the-art control approaches based on system identification and contextual optimization. Finally, using the scenario of an F-16 aircraft diving towards the ground, we show how DaTaControl prevents a ground collision using only the measurements obtained during the dive and elementary laws of physics as side information.