  In this work we developed a deep learning technique that successfully solves
a non-linear dynamic control problem. Instead of directly tackling the control
problem, we combined methods in probabilistic neural networks and a
Kalman-Filter-inspired model to build a non-linear state estimator for the
system. We then used the estimated states to implement a trivial controller for
the now fully observable system. We applied this technique to a crucial
non-linear control problem that arises in the operation of the LIGO system, an
interferometric gravitational-wave observatory. We demonstrated in simulation
that our approach can learn from data to estimate the state of the system,
allowing a successful control of the interferometer's mirror . We also
developed a computationally efficient model that can run in real time at high
sampling rate on a single modern CPU core, one of the key requirements for the
implementation of our solution in the LIGO digital control system. We believe
these techniques could be used to help tackle similar non-linear control
problems in other applications.
