  We present differentiable predictive control (DPC), a method for learning
constrained neural control policies for linear systems with probabilistic
performance guarantees. We employ automatic differentiation to obtain direct
policy gradients by backpropagating the model predictive control (MPC) loss
function and constraints penalties through a differentiable closed-loop system
dynamics model. We demonstrate that the proposed method can learn parametric
constrained control policies to stabilize systems with unstable dynamics, track
time-varying references, and satisfy nonlinear state and input constraints. In
contrast with imitation learning-based approaches, our method does not depend
on a supervisory controller. Most importantly, we demonstrate that, without
losing performance, our method is scalable and computationally more efficient
than implicit, explicit, and approximate MPC.
  Under review at IEEE Transactions on Automatic Control.
