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

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 N=1$$ N=1 $$ 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.