Approximate Closed-Loop Robust Model Predictive Control With Guaranteed Stability and Constraint Satisfaction

Abstract

The real-time implementation of closed-loop robust model predictive control (MPC) schemes is an important challenge for fast systems, as their solution complexity depends strongly on the system size, control policy parametrization, and prediction horizon. We look to address this problem by approximating the implicitly-defined MPC controller using deep learning. Although the resulting neural network approximation has a small memory footprint and can be efficiently computed, it does not guarantee robust constraint satisfaction or stability. We propose a novel projection-based strategy that is capable of providing a certificate of robust feasibility and input-to-state stability in real-time. We also show how this projection operator can be formulated as a parametric quadratic program that is solvable offline. The advantages of the proposed approach are demonstrated on a benchmark case study.