A Survey on Sensitivity-based Nonlinear Model Predictive Control

Abstract

This survey explores recent results in the development of optimization algorithms and formulations for moving horizon estimation (MHE), nonlinear model predictive control (NMPC) and dynamic real-time optimization (D-RTO), with extrapolative nonlinear dynamic (e.g., first principle) models. We consider Nonlinear Programming (NLP) and NLP sensitivity as natural tools for formulation and efficient solution of optimization problems for these three tasks. For MHE, we develop a maximum likelihood formulation that directly incorporates nonlinear models, and is seamlessly adapted to updating the arrival costs. This approach is also extended easily to M-estimators, which essentially eliminate biased estimates due to gross errors. For NMPC, we develop formulations that incorporate well-understood stability and robustness properties, even for large, complex plant models. Finally, recent work has extended these capabilities from setpoint tracking objectives to more general stage costs that are economically based, thus leading to a robustly stable strategy for D-RTO. In concert with these problem formulations, the realization of MHE, NMPC and D-RTO requires the application of a fast NLP solver for time-critical, on-line optimization, as well as efficient NLP sensitivity tools that eliminate computational delay, and guarantee stability and robustness. Algorithms that meet these demands are explored and outlined for these tasks. Finally, a number of challenging distillation case studies are presented that demonstrate the effectiveness of these optimization-based strategies.