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We investigate the problem of data-driven, on-the-fly control of systems withunknown nonlinear dynamics where data from only a single finite-horizontrajectory and possibly side information on the dynamics are available. Suchside information may include knowledge of the regularity of the dynamics,monotonicity of the states, or decoupling in the dynamics between the states.Specifically, we develop two algorithms, $\texttt{DaTaReach}$ and$\texttt{DaTaControl}$, to over-approximate the reachable set and designcontrol signals for the system on the fly. $\texttt{DaTaReach}$ constructs adifferential inclusion that contains the unknown vector field. Then, itcomputes an over-approximation of the reachable set based on intervalTaylor-based methods applied to systems with dynamics described as differentialinclusions. $\texttt{DaTaControl}$ enables convex-optimization-based,near-optimal control using the computed over-approximation and thereceding-horizon control framework. We provide a bound on its suboptimality andshow that more data and side information enable $\texttt{DaTaControl}$ toachieve tighter suboptimality bounds. Finally, we demonstrate the efficacy of$\texttt{DaTaControl}$ over existing approaches on the problems of controllinga unicycle and quadrotor systems.

On-The-Fly Control of Unknown Smooth Systems from Limited Data