Learning Convex Terminal Costs for Complexity Reduction in MPC

Despite recent advances in computing hardware and optimization algorithms, solving model predictive control (MPC) problems in real time still poses some technical challenges when long prediction and control horizons are used, due to the presence of several optimization variables and constraints. In this paper, we propose to reduce the computational burden by shortening the prediction and control horizon to a single step while preserving good closed-loop performance. This is achieved by using machine learning techniques to construct a tailored quadratic and convex terminal cost that approximates the cost-to-go function of constrained linear (possibly parameter-dependent) MPC formulations. The potentials of the proposed MPC with Learned Terminal Cost (LTC-MPC) approach is demonstrated in two numerical examples.