Nonlinear Programming Formulations for Nonlinear and Economic Model Predictive Control

We present a framework for constructing robust nonlinear model predictive controllers (NMPCs) with either tracking or economic objectives. For this, we explore properties of nonlinear programming problems (NLPs) that arise in the formulation of NMPC subproblems and show their influence on stability and robustness properties. In particular, NLPs that satisfy the Mangasarian-Fromovitz constraint qualification (MFCQ), the constant rank constraint qualification (CRCQ), and generalized strong second order sufficient conditions (GSSOSC) have solutions that are continuous with respect to perturbations of the problem data. These are important prerequisites for nominal and robust 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 ℓ 1 penalty terms. We also show how these properties …