  In this paper, we propose a novel framework for approximating the explicit
MPC policy for linear parameter-varying systems using supervised learning. Our
learning scheme guarantees feasibility and near-optimality of the approximated
MPC policy with high probability. Furthermore, in contrast to most existing
approaches that only learn the MPC policy, we also learn the "dual policy",
which enables us to keep a check on the approximated MPC's optimality online
during the control process. If the check deems the control input from the
approximated MPC policy safe and near-optimal, then it is applied to the plant,
otherwise a backup controller is invoked, thus filtering out (severely)
suboptimal control inputs. The backup controller is only invoked with a bounded
(low) probability, where the exact probability level can be chosen by the user.
Since our framework does not require solving any optimization problem during
the control process, it enables the deployment of MPC on resource-constrained
systems. Specifically, we illustrate the utility of the proposed framework on a
vehicle dynamics control problem. Compared to online optimization methods, we
demonstrate a speedup of up to 62x on a desktop computer and 10x on an
automotive-grade electronic control unit, while maintaining a high control
performance.
