Fast sensitivity-based economic model predictive control for degenerate systems

Abstract

We present a sensitivity-based nonlinear model predictive control (NMPC) algorithm and demonstrate it on a case study with an economic cost function. In contrast to existing sensitivity-based approaches that make strong assumptions on the underlying optimization problem (e.g. the linear independence constraint qualification implying unique multiplier), our method is designed to handle problems satisfying a weaker constraint qualification, namely the Mangasarian-Fromovitz constraint qualification (MFCQ). Our nonlinear programming (NLP) sensitivity update consists of three steps. The first step is a corrector step in which a system of linear equations is solved. Then a predictor step is computed by a quadratic program (QP). Finally, a linear program (LP) is solved to select the multipliers that give the correct sensitivity information. A path-following scheme containing these steps is embedded in the advanced-step NMPC (asNMPC) framework. We demonstrate our method on a large-scale case example consisting of a reactor and distillation process. We show that LICQ does not hold and the path-following method is able to accurately approximate the ideal solutions generated by an NLP solver.