Unsupervised closed-loop primal-dual learning of approximate model predictive controllers

Model predictive control (MPC) is a powerful control strategy capable of handling constrained nonlinear systems. However, the need for the repeated online solution of optimization problems can be a significant challenge for its real-time application. To address this issue we employ neural network approximations of the MPC control law, which can be swiftly evaluated. Typical supervised training strategies require the solution of large amounts of optimization problems for the generation of training data. To avoid this requirement, we propose an unsupervised closed-loop primal-dual learning strategy, which ensures training data from relevant areas of the state-space without sampling of optimizer solutions. Furthermore, primal-dual learning reduces the importance of manually tuned penalty parameters by using learned Lagrange multipliers. The performance of the proposed strategy is investigated in the context of crosswind kite control, showing comparable performance to nominal MPC while significantly reducing the computational complexity.