  This paper focuses on developing a strategy for control of systems whose
dynamics are almost entirely unknown. This situation arises naturally in a
scenario where a system undergoes a critical failure. In that case, it is
imperative to retain the ability to satisfy basic control objectives in order
to avert an imminent catastrophe. A prime example of such an objective is the
reach-avoid problem, where a system needs to move to a certain state in a
constrained state space. To deal with limitations on our knowledge of system
dynamics, we develop a theory of myopic control. The primary goal of myopic
control is to, at any given time, optimize the current direction of the system
trajectory, given solely the information obtained about the system until that
time. We propose an algorithm that uses small perturbations in the control
effort to learn local dynamics while simultaneously ensuring that the system
moves in a direction that appears to be nearly optimal, and provide hard bounds
for its suboptimality. We additionally verify the usefulness of the algorithm
on a simulation of a damaged aircraft seeking to avoid a crash, as well as on
an example of a Van der Pol oscillator.
