Deep Model Predictive Control with Stability Guarantees

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 neural network (DNN) is employed to approximate them. In order to avoid any unwanted behavior during the learning phase, a tube-based nonlinear 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 the origin under certain conditions. To make the algorithm implementable online, a dual-timescale adaptation mechanism is utilized, where the weights of the output layer of the neural network are updated each time instant using a weight update law, while the inner layers are repeatedly trained in self-supervised manner by using the adaptive actions as labels for the training. Our results are validated through a numerical experiment, which indicates that the proposed deep MPC architecture is effective in learning to control safety critical systems without suffering instability drawbacks.