Nonlinear model predictive control (NMPC) with first principle models has recently received a great amount of attention from industry. However, the inherited barriers to this control strategy are the large on-line computational cost and resulting feedback delays. To overcome some of these limitations, the so-called advanced-step NMPC controller (AS-NMPC) has been recently proposed. The controller makes use of the dynamic model to predict the future state of the system, use this state to solve a predicted problem in advance and correct on-line using a fast NLP sensitivity approximation. It has been reported in several large-scale applications that the AS-NMPC controller is able to reduce the feedback delay by at least two orders of magnitude compared to the on-line solution of the full NMPC problem and that the sensitivity approximation errors are negligible [1,4]. Moreover, it has been shown that the AS-NMPC controller enjoys the same nominal stability properties of a standard or ideal NMPC controller and its inherent robust stability properties have also been established [3].

If high degrees of uncertainty are present in the system, the inherent robust stability properties of NMPC are not sufficient. In this case, robust design strategies able to account for uncertainty explicitly in the controller formulation are required. Several formulations have been summarized in [2]. It has been shown that the Min-Max NMPC formulation, which computes the best control policy based on the worst expected realization of the uncertainties, is able to guarantee robust stability. This controller formulation is attractive from a theoretical point of view but dramatically increases the computational cost of the on-line NMPC problem. From a computational point of view, more attractive alternatives based on multi-scenario formulations and linearization arguments have been proposed.

In this work, we explore different robust NMPC formulations and embed them into the AS-NMPC controller framework. In particular, we emphasize on the benefits of multi-scenario formulations due to their favorable structure and we explore different strategies to capture the full uncertainty description using a few scenarios. Finally, we explore connections to state estimation that allows a further reduction of the number of scenarios. Simulation examples are presented to demonstrate the concepts.

Reference:

[1] R. Huang, V.M. Zavala, and L.T. Biegler. Advanced step nonlinear model predictive control for air separation units. Submitted for Publication.

[2] L. Magni and R. Scattolini. Robustness and robust design of mpc for nonlinear discrete-time systems. In R. Findeisen, F. Allgöwer, and L.T Biegler, editors, Assessment and Future Directions of Nonlinear Model Predictive Control, pages 239{254. Springer, 2007.

[3] V.M. Zavala and L.T. Biegler. The advanced step nmpc controller: Optimality, stability and robustness. Automatica, Submitted for publication, 2007.

[4] V.M. Zavala, C.D. Laird, and L.T. Biegler. Fast implementations and rigorous models: Can both be accommodated in nmpc? Int. J. Robust Nonlinear Control, 18:800-815, 2008.