(256a) Stability and Performance Analysis of Nlp Sensitivity-Based Nmpc Controllers

One of the basic premises behind any control strategy is to provide fast feedback to the plant in order to achieve a desired performance. This basic premise is, on the other hand, one of the main limitations associated to computationally intensive control strategies such as NMPC.

NMPC is a feedback control strategy that is based on the on-line solution of an optimal control problem (OCP). As industrial NMPC applications demand the incorporation of increasingly larger and detailed dynamic process models [1,2], the development of efficient numerical methods for the solution of large-scale OCPs has become fundamental. While advances in optimization strategies and algorithms have enabled the solution of increasingly larger OCPs, on-line implementations of NMPC still represent a challenge [3]. This is particularly true in large-scale applications where the solution of the OCP takes a non-negligible amount of time, giving rise to computational delays.

The effect of computational delays on the performance of NMPC has been noted by Santos et.al. in a laboratory reactor [4] as well as in numerous industrial studies. Deterioration of stability has been also noted by Findeisen and Allgöwer which provide a detailed stability analysis in [5]. To address this issue, several real-time NMPC strategies have been proposed. Neighboring extremals, Newton-step controllers and NLP sensitivity-based controllers represent some alternatives. On the other hand, an issue associated to these strategies is the impact of suboptimality on the controller performance and stability properties.

In this work, we analyze the nominal and robust stability properties of previously reported NLP sensitivity-based NMPC controllers [6]. In particular, a new NLP sensitivity-based controller is presented. The main result is that this real-time controller enjoys of the same nominal stability properties of the ideal NMPC controller. As a consequence, an analysis of its inherent robustness properties can be performed through input-to-state stability (ISS) and NLP sensitivity concepts in a straightforward manner. These concepts are also used to establish a general stability analysis framework for NLP sensitivity-based controllers. In addition, practical issues related to the implementation of NLP sensitivity capabilities on large-scale NLP solvers are discussed. Computational results are presented to illustrate the potential of the presented ideas. At the same time, special emphasis is made on their limitations in order to motivate ideas for future research.

[1] Bartusiak, R.D. NLMPC: A platform for optimal control of feed- or product-flexible manufacturing. In Assessment and Future Directions of NMPC. Springer, Berlin, 2007.

[2] Nagy, Z.K., R. Franke, B. Mahn, and F. Allgöwer. Real-time implementation of nonlinear model predictive control of batch processes in an industrial framework. In Assessment and Future Directions of NMPC. Springer, Berlin, 2007.

[3] Biegler, L.T. Efficient solution of dynamic optimization and NMPC problems. In Nonlinear Model Predictive Control. Birkhauser, Basel, 2000.

[4] Santos, L.O., P. Afonso, J. Castro, N. Oliveira, and L. T. Biegler. On-line implementation of Nonlinear MPC: An experimental case study. Control Engineering Practice, 9, 2001.

[5] Findeisen R. and F. Allgöwer. Computational delay in nonlinear model predictive control. Proc. Int. Symp. Adv. Control of Chemical Processes, ADCHEM'03, 2004.

[6] Zavala, V.M., C.D. Laird and L.T. Biegler. Fast implementations and rigorous models: Can both be accommodated in NMPC? Int. Journal of Robust and Nonlinear Control, Accepted for Publication . 2007.