  This paper presents a deep learning based model predictive control (MPC)
algorithm for systems with unmatched and bounded state-action dependent
uncertainties of unknown structure. We utilize a deep neural network (DNN) as
an oracle in the underlying optimization problem of learning based MPC (LBMPC)
to estimate unmatched uncertainties. Generally, non-parametric oracles such as
DNN are considered difficult to employ with LBMPC due to the technical
difficulties associated with estimation of their coefficients in real time. We
employ a dual-timescale adaptation mechanism, where the weights of the last
layer of the neural network are updated in real time while the inner layers are
trained on a slower timescale using the training data collected online and
selectively stored in a buffer. Our results are validated through a numerical
experiment on the compression system model of jet engine. These results
indicate that the proposed approach is implementable in real time and carries
the theoretical guarantees of LBMPC.
