1

We provide a case study for DaTaReach and DaTaControl, algorithms for reachability analysis and control of systems with a priori unknown nonlinear dynamics. In a scenario involving an F-16 aircraft diving towards the ground from low altitude and high downward pitch angle, we show how DaTaControl prevents a ground collision using only the measurements obtained during the dive and elementary laws of physics as side information.

We develop a control algorithm for the safety of a control-affine system with unknown nonlinear dynamics in the sense of confinement in a given safe set. The algorithm leverages robust nonlinear feedback control laws integrated with on-the-fly, data-driven approximations to output a control signal that guarantees the boundedness of the closed-loop system in the given set.

We develop two data-driven algorithms, DaTaReach and DaTaControl, for the on-the-fly over-approximation of the reachable set and constrained near-optimal control of systems with unknown dynamics. These algorithms are suitable for scenarios with severely limited data by leveraging various forms of side information on the underlying unknown dynamics.

As the number of agents comprising a swarm increases, individual-agent-based control techniques for collective task completion become computationally intractable. Instead, we develop an algorithm, agnostic to the size of the swarm, to control, in a decentralized and probabilistic manner, a collective property of the swarm: its density distribution constrained with high-level task specifications expressed in temporal logic.