  The application of supervised learning techniques in combination with model
predictive control (MPC) has recently generated significant interest,
particularly in the area of approximate explicit MPC, where function
approximators like deep neural networks are used to learn the MPC policy via
optimal state-action pairs generated offline. While the aim of approximate
explicit MPC is to closely replicate the MPC policy, substituting online
optimization with a trained neural network, the performance guarantees that
come with solving the online optimization problem are typically lost. This
paper considers an alternative strategy, where supervised learning is used to
learn the optimal value function offline instead of learning the optimal
policy. This can then be used as the cost-to-go function in a myopic MPC with a
very short prediction horizon, such that the online computation burden reduces
significantly without affecting the controller performance. This approach
differs from existing work on value function approximations in the sense that
it learns the cost-to-go function by using offline-collected state-value pairs,
rather than closed-loop performance data. The cost of generating the
state-value pairs used for training is addressed using a sensitivity-based data
augmentation scheme.
