  We present differentiable predictive control (DPC) as a deep learning-based
alternative to the explicit model predictive control (MPC) for unknown
nonlinear systems. In the DPC framework, a neural state-space model is learned
from time-series measurements of the system dynamics. The neural control policy
is then optimized via stochastic gradient descent approach by differentiating
the MPC loss function through the closed-loop system dynamics model. The
proposed DPC method learns model-based control policies with state and input
constraints, while supporting time-varying references and constraints. In
embedded implementation using a Raspberry-Pi platform, we experimentally
demonstrate that it is possible to train constrained control policies purely
based on the measurements of the unknown nonlinear system. We compare the
control performance of the DPC method against explicit MPC and report
efficiency gains in online computational demands, memory requirements, policy
complexity, and construction time. In particular, we show that our method
scales linearly compared to exponential scalability of the explicit MPC solved
via multiparametric programming.
