  Model predictive control (MPC) is a powerful control method that handles
dynamical systems with constraints. However, solving MPC iteratively in real
time, i.e., implicit MPC, remains a computational challenge. To address this,
common solutions include explicit MPC and function approximation. Both methods,
whenever applicable, may improve the computational efficiency of the implicit
MPC by several orders of magnitude. Nevertheless, explicit MPC often requires
expensive pre-computation and does not easily apply to higher-dimensional
problems. Meanwhile, function approximation, although scales better with
dimension, still requires pre-training on a large dataset and generally cannot
guarantee to find an accurate surrogate policy, the failure of which often
leads to closed-loop instability. To address these issues, we propose a
triple-mode hybrid control scheme, named Memory-Augmented MPC, by combining a
linear quadratic regulator, a neural network, and an MPC. From its standard
form, we further derive two variants of such hybrid control scheme: one
customized for chaotic systems and the other for slow systems. The proposed
scheme does not require pre-computation and can improve the amortized running
time of the composed MPC with a well-trained neural network. In addition, the
scheme maintains closed-loop stability with any neural networks of proper input
and output dimensions, alleviating the need for certifying optimality of the
neural network in safety-critical applications.
