  Determining the reachable set for a given nonlinear control system is crucial
for system control and planning. However, computing such a set is impossible if
the system's dynamics are not fully known. This paper is motivated by a
scenario where a system suffers an adverse event mid-operation, resulting in a
substantial change to the system's dynamics, rendering them largely unknown.
Our objective is to conservatively approximate the system's reachable set
solely from its local dynamics at a single point and the bounds on the rate of
change of its dynamics. We translate this knowledge about the system dynamics
into an ordinary differential inclusion. We then derive a conservative
approximation of the velocities available to the system at every system state.
An inclusion using this approximation can be interpreted as a control system;
the trajectories of the derived control system are guaranteed to be
trajectories of the unknown system. To illustrate the practical implementation
and consequences of our work, we apply our algorithm to a simplified model of
an unmanned aerial vehicle.
