Learning Lyapunov terminal costs from data for complexity reduction in nonlinear model predictive control

Abstract A classic way to design a nonlinear model predictive control (NMPC) scheme with guaranteed stability is to incorporate a terminal cost and a terminal constraint into the problem formulation. While a long prediction horizon is often desirable to obtain a large domain of attraction and good closed‐loop performance, the related computational burden can hinder its real‐time deployment. In this article, we propose an NMPC scheme with prediction horizon and no terminal constraint to drastically decrease the numerical complexity without significantly impacting closed‐loop stability and performance. This is attained by constructing a suitable terminal cost from data that estimates the cost‐to‐go of a given NMPC scheme with long prediction horizon. We demonstrate the advantages of the proposed control scheme in two benchmark control problems.