Nonlinear Programming Properties for Stable and Robust NMPC

Abstract

We explore properties of nonlinear programming problems (NLPs) that arise in the formulation of NMPC subproblems and show their influence on stability and robustness of NMPC. NLPs that satisfy linear independence constraint qualification (LICQ), second order sufficient conditions (SOSC) and strict complementarity (SC), have solutions that are continuous and differentiable with perturbations of the problem data. As a result, they are important prerequisites for nominal and ISS stability of NMPC controllers. Moreover, we show that ensuring these properties is possible through reformulation of the NLP subproblem for NMPC, through the addition of l1 penalty and barrier terms. We show how these properties also establish ISS of related sensitivity-based NMPC controllers, such as asNMPC and amsNMPC. Finally, we demonstrate the impact of our reformulated NLPs on several examples that have shown nonrobust performance on earlier NMPC strategies.