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We develop data-driven algorithms for reachability analysis and control ofsystems with a priori unknown nonlinear dynamics. The resulting algorithms notonly are suitable for settings with real-time requirements but also provideprovable performance guarantees. To this end, they merge noisy data from only asingle finite-horizon trajectory and, if available, various forms of sideinformation. Such side information may include knowledge of the regularity ofthe dynamics, algebraic constraints on the states, monotonicity, or decouplingin the dynamics between the states. Specifically, we develop two algorithms,$\texttt{DaTaReach}$ and $\texttt{DaTaControl}$, to over-approximate thereachable set and design control signals for the system on the fly.$\texttt{DaTaReach}$ constructs a differential inclusion that contains theunknown dynamics. Then, in a discrete-time setting, it over-approximates thereachable set through interval Taylor-based methods applied to systems withdynamics described as differential inclusions. We provide a bound on the timestep size that ensures the correctness and termination of $\texttt{DaTaReach}$.$\texttt{DaTaControl}$ enables convex-optimization-based control using thecomputed over-approximation and the receding-horizon control framework.Besides, $\texttt{DaTaControl}$ achieves near-optimal control and is suitablefor real-time control of such systems. We establish a bound on itssuboptimality and the number of primitive operations it requires to computecontrol values. Then, we theoretically show that $\texttt{DaTaControl}$achieves tighter suboptimality bounds with an increasing amount of data andricher side information. Finally, experiments on a unicycle, quadrotor, andaircraft systems demonstrate the efficacy of both algorithms over existingapproaches.

On-The-Fly Control of Unknown Systems: From Side Information to Performance Guarantees through Reachability