Finite-step Terminal Ingredients for Stabilizing Model Predictive Control

This paper proposes a novel construction of the terminal cost and terminal set in stabilizing model predictive control that uses finite-step Lyapunov functions and finite-step invariant sets. This construction results in a periodic terminal set constraint associated with a finite sequence of terminal sets, out of which none is required to be invariant. We argue that constructing such sets is easier and more scalable compared to invariant sets, while a comparable region of attraction is obtained for the same prediction horizon. In the one step case the proposed stability conditions reduce naturally to the standard terminal cost and constraint set stability conditions.