Safe Explicit MPC by Training Neural Networks Through Constrained Optimization

Faster execution times achievable with explicit model predictive control (EMPC) promise to further extend the applicability of MPC. This work presents a novel approach for developing safe EMPC by training a neural network through a constrained optimization problem. Unique to this approach is the incorporation of closedloop safety constraints directly into the neural network training step. Tractable training times are achieved since the number of points at which constraints are evaluated can be scaled with low computational cost, and the training problem is solved using a first order primal-dual method. The approach generalizes to nonlinear dynamics and constraints. Simulation experiments on three different systems demonstrate that the approach is capable of achieving approximately optimal, safe closed-loop control while requiring three to four orders of magnitude reduced time for online evaluation.