Fast Sensitivity-Based Nonlinear Economic Model Predictive Control with Degenerate NLP

Abstract

We present a fast sensitivity-based nonlinear model predictive control (NMPC) algorithm, that can handle non-unique multipliers in the discretized dynamic optimization problem. Non-unique multipliers may arise, for example when path constraints are active for longer periods of the prediction horizon. This is a common situation in economic model predictive control. In such cases, the optimal nonlinear programming (NLP) solution often satisfies the Mangasarian-Fromovitz constraint qualification (MFCQ), which implies non-unique, but bounded multipliers. Consequently, any sensitivity-based fast NMPC scheme must allow for discontinuous jumps in the multipliers. In this paper, we apply a sensitivity-based path-following algorithm that allows multiplier jumps within the advance-step NMPC (asNMPC) framework. The path-following method consists of a corrector and a predictor step, which are computed by solving a system of linear equations, and a quadratic programming problem, respectively, and a multiplier jump step determined by the solution of a linear program. We demonstrate the proposed method on an economic NMPC case study with a CSTR.