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 l1 penalty terms. We also show how these properties extend beyond tracking objective functions to economic NMPC (eNMPC), a more general dynamic optimization problem, where further reformulation is required for stability guarantees. We present and discuss the relative merits of three alternative methods for stabilizing eNMPC: objective regularization based on the full state-space, objective regularization based on a reduced set of states, and the addition of a stabilizing constraint. Finally, we demonstrate these eNMPC formulations on a continuously stirred tank reactor (CSTR) as well as a pair of coupled distillation columns.