(389g) Online Model Maintenance and Robust Adaptive Nonlinear Model Predictive Control

Nonlinear model predictive control (NMPC) has received a great amount of attention from both industry and academia in the last two decades. Here, the prediction model, which is the key to the success of NMPC applications, is usually developed during the implementation step. However, as time progresses or operating conditions change drastically, some of the plant parameters can change dramatically from their nominal values, which leads to significant plant model-mismatches.

One Passive way to deal this situation is to keep the same nominal model but to use various robust NMPC strategies. For example, we proposed a robust NMPC strategy based on solving a multi-scenario problem in [1], as well as a robust NMPC scheme incorporating the observer errors [2], which also provides offset free regulatory behavior. Other robust NMPC strategies, including min-max formulation and reachable sets, or tubes, have also been proposed, as summarized in [3]. Another active alternative is to retain the nominal NMPC strategy but to adapt the model parameters online. Since this actively changes the prediction model, online model maintenance has long term benefits of NMPC schemes [5]. A conventional scheme to estimate the model parameters is through the introduction of additional artificial states in the state observer (e.g., Chapter 5 in [4]). A limitation of this scheme is that a subset of parameters that are estimated on-line is fixed. Recently, Deshpande et al. [5] proposed an online model maintenance approach based on generalized likelihood ratio method, which overcomes this limitation. Both approaches lead to adaptive NMPC formulations, although their stability characteristics have not been adequately investigated in the literature.

In this work, we propose a scheme to update the model parameter online by minimizing the variance of previous observer errors over a moving time horizon. This facilitates model maintenance in both the observer and controller. We integrate this state and parameter estimator within a NMPC formulation, for which robust stability can be established, leading to an adaptive NMPC strategy. We also propose to integrate the concept of terminal state proposed in [6] with the adaptive NMPC formulation. Moreover, this adaptive strategy ensures that the observer's error converges to zero and controller is asymptotically stable, even in the presence of drastic changes in model parameters. Advantages of the proposed method are shown through simulation.

Reference:

[1] R. Huang, S. Patwardhan and L. Biegler. Multi-scenario based robust nonlinear model predictive control with first principle dynamic models. 10th International Symposium on Process Systems Engineering. Accepted for publication, 2009.

[2] R. Huang, S. Patwardhan and L. Biegler. Robust Extended Kalman Filter Based Nonlinear Model Predictive Control Formulation. Submitted for publication, 2009.

[3] D. Limon, T. Alamo, D.M. Raimondo, D.M.de la Peña, J.M. Bravo and E.F. Camacho. Input-to-state stability: a unifying framework for robust model predictive control. In Assessment and Future Directions of NMPC. In Press, Springer, 2008.

[4] D. Seborg and M. Henson. Nonlinear Process Control. Prentice Hall, 1997.

[5] A. Deshpande, S. Patwardhan and S. Narasimhan. Intelligent state estimation for fault tolerant nonlinear predictive control. J. of Process Control. 2009, 19: 187.

[6] H. Chen and F. Allgöwer. A quasi infinite horizon nonlinear model predictive control scheme with guaranteed stability. Automatica. 1998, 34:1205.