We investigate the problem of data-driven, on-the-fly control of systems with unknown nonlinear dynamics wheredata from only a single finite-horizon trajectory and possibly side information on the dynamics are available. Such side information may include knowledge of the regularity of the underlying dynamics, monotonicity, or decoupling in the dynamics between the states. Specifically, we propose two algorithms, DaTaReach and DaTaControl, to over-approximate the reachable set and design control signals for the system on the fly. DaTaReach constructs a differential inclusion that contains the unknown dynamics. Then, it computes an over-approximation of the reachable set-based on interval Taylor-based methods applied to systems with dynamics described as differential inclusions. DaTaControl enables convex-optimization-based, near-optimal control using the computed over-approximation and the receding-horizon control framework. We provide a bound on its suboptimality and show that more data and side information enable DaTaControl to achieve tighter suboptimality bounds. Finally, we demonstrate the efficacy of DaTaControl over existing approaches on the problem of controlling the F-16 model.
Keywords: Data-driven control, F-16, Reachable set computation