Composing MPC with LQR and Neural Networks for Efficient and Stable Control

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, has been a challenge for 1) systems with low-latency requirements, 2) systems with limited computational resources, and 3) systems with fast and complex dynamics. To address this challenge, for lowdimensional linear systems, a classical approach is explicit MPC; for high-dimensional or nonlinear systems, a common approach is function approximation using neural networks. Both methods, whenever applicable, may improve the computational efficiency of the original MPC by several orders of magnitude. The existing methods have the following disadvantages: 1) explicit MPC does not apply to higher-dimensional problems or most of the problems with nonlinear constraints; and 2) function approximation is not guaranteed to find an accurate surrogate policy, the failure of which may lead to closed-loop instability. To address these issues, we propose a triple-mode hybrid control scheme, named Memory-Augmented MPC, by combining an efficient linear quadratic regulator, an efficient neural network, and a costly, fail-safe MPC. From its standard form, we derive two variants of such hybrid control scheme: one customized for chaotic systems and the other for slow systems. We prove stability of the control scheme with any arbitrary neural networks and test its computational performance in simulated numerical experiments.