Deep unfolding projected first order methods-based architectures: application to linear model predictive control

Deep learning black-box neural networks have revolutionized many fields, including image processing, inverse problems, text mining and more recently, give very promising results in systems and control. Recently, unfolded deep learning techniques were proposed, which bring the physics of the model and standard optimization techniques into the architecture design, in order to eliminate the disadvantages of the black-box learning. In this paper we design trainable unfolded deep architectures for linear MPC based on two standard iterative optimization algorithms (projected gradient descent-PGD and accelerated projected gradient descent - APGD). Our neural networks are expressed as the combination of weight and activation functions with closed-form expressions and an extra parameter allowing to consider the basic algorithm (PGD) or its accelerated version (APGD). We also study the performance of the proposed networks on a linear MPC application.