  This paper presents a deep learning based model predictive control algorithm
for control affine nonlinear discrete time systems with matched and bounded
state dependent uncertainties of unknown structure. Since the structure of
uncertainties is not known, a deep learning based adaptive mechanism is
utilized to mitigate disturbances. In order to avoid any unwanted behavior
during the learning phase, a tube based model predictive controller is
employed, which ensures satisfaction of constraints and input-to-state
stability of the closed-loop states. In addition, the proposed approach
guarantees the convergence of states to origin under certain verifiable
conditions. To ensure stability and undesirable learning transients, a
dual-timescale adaptation mechanism is proposed, where the weights of the last
layer of the neural network are updated each time instant while the inner
layers are trained on a slower timescale using training data collected online
and selectively stored in a buffer on the basis of singular value maximization
criterion. Our results are validated through numerical experiments on wing-rock
dynamics. These results indicate that the proposed deep-MPC architecture is
effective in learning to control safety critical systems without suffering
instability drawbacks.
