  We present a differentiable predictive control (DPC) methodology for learning
constrained control laws for unknown nonlinear systems. DPC poses an
approximate solution to multiparametric programming problems emerging from
explicit nonlinear model predictive control (MPC). Contrary to approximate MPC,
DPC does not require supervision by an expert controller. Instead, a system
dynamics model is learned from the observed system's dynamics, and the neural
control law is optimized offline by leveraging the differentiable closed-loop
system model. The combination of a differentiable closed-loop system and
penalty methods for constraint handling of system outputs and inputs allows us
to optimize the control law's parameters directly by backpropagating economic
MPC loss through the learned system model. The control performance of the
proposed DPC method is demonstrated in simulation using learned model of
multi-zone building thermal dynamics.
