LAUSR

Abstract The analysis of convergence and stability conditions for Non-linear Model Predictive Control (NMPC) schemes has seen significant progress during the last decades. Numerous results in the literature state sufficient conditions for convergence and/or stability of NMPC. Yet, necessary and sufficient conditions are—to the best of the author’s knowledge—not known and, given the variety of choices for MPC design, seemingly appear to be difficult. This paper analyzes the convergence of NMPC of continuous-time systems in time-invariant settings. We introduce the receding-horizon Hamiltonian—i.e., the value of the optimal control Hamiltonian along the sequence of OCPs—as a novel tool for stability/convergence analysis. Based on the assumption of strict dissipativity, we prove necessary and sufficient conditions for asymptotic convergence of the closed loop to the optimal steady state. Numerical results obtained for the Van de Vusse reactor illustrate the proposed conditions.