Abstract
Sensitivity-based strategies for on-line moving horizon estimation (MHE) and nonlinear model predictive control (NMPC) are presented both from a stability and computational perspective. These strategies make use of full-space interior-point nonlinear programming (NLP) algorithms and NLP sensitivity concepts. In particular, NLP sensitivity allows us to partition the solution of the optimization problems into background and negligible on-line computations, thus avoiding the problem of computational delay even with large dynamic models. We demonstrate these developments through a distributed polymerization reactor model containing around 10,000 differential and algebraic equations (DAEs).
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References
Wächter, A., Biegler, L.T.: On The Implementation of an Interior-Point Filter Line-Search Algorithm for Large-Scale Nonlinear Programming. Math. Programm. 106, 25–57 (2006)
Zavala, V.M., Biegler, L.T.: The Advanced Step NMPC Controller: Stability, Optimality and Robustness. Automatica (to appear) (2008)
Zavala, V.M., Laird, C.D., Biegler, L.T.: Fast Implementations and Rigorous Models: Can Both be Accommodated in NMPC? Int. Journal of Robust and Nonlinear Control 18, 800–815 (2008)
Schäfer, A., Kühl, P., Diehl, M., Schlöder, J., Bock, H.G.: Fast reduced multiple shooting methods for nonlinear model predictive control. Chemical Engineering and Processing 46, 1200–1214 (2007)
Duff, I.S.: MA57 - A Code for the Solution of Sparse Symmetric Definite and Indefinite Systems. ACM Transactions on Mathematical Software 30, 118–144 (2004)
Karypis, G., Kumar, V.: A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs. SIAM J. Sci. Comput. 20, 359–392 (1999)
Fiacco, A.V.: Introduction to Sensitivity and Stability Analysis in Nonlinear Programming. Academic Press, New York (1983)
Büskens, C., Maurer, H.: Sensitivity Analysis and Real-Time Control of Parametric Control Problems Using Nonlinear Programming Methods. In: Grötschel, M., et al. (eds.) On-line Optimization of Large-scale Systems. Springer, Berlin (2001)
Bartlett, R.A., Biegler, L.T., Backstrom, J., Gopal, V.: Quadratic Programming Algorithms for Large-Scale Model Predictive Control. Journal of Process Control 12, 775–795 (2002)
Zavala, V.M., Laird, C.D., Biegler, L.T.: A Fast Moving Horizon Estimation Algorithm Based on Nonlinear Programming Sensitivity. Journal of Process Control 18, 876–884 (2008)
Findeisen, R., Diehl, M., Burner, T., Allgöwer, F., Bock, H.G., Schlöder, J.P.: Efficient Output Feedback Nonlinear Model Predictive Control. In: Proceedings of American Control Conference, vol. 6, pp. 4752–4757 (2002)
Muske, K.R., Meadows, E.S., Rawlings, J.B.: The Stability of Constrained Receding Horizon Control with State Estimation. In: Proceedings of American Control Conference, vol. 3, pp. 2837–2841 (1994)
Zavala, V.M., Biegler, L.T.: Large-Scale Nonlinear Programming Strategies for the Operation of Low-Density Polyethylene Tubular Reactors. In: Proceedings of ESCAPE 18, Lyon (2008)
Zavala, V.M., Biegler, L.T.: Optimization-Based Strategies for the Operation of Low-Density Polyethylene Tubular Reactors: Moving Horizon Estimation. Comp. and Chem. Eng. (in press) (2008)
Alessandri, A., Baglietto, M., Battistelli, G.: Moving-Horizon State Estimation for Nonlinear Discrete-Time Systems: New Stability Results and Approximation Schemes. Automatica 44, 1753–1765 (2008)
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Zavala, V.M., Biegler, L.T. (2009). Nonlinear Programming Strategies for State Estimation and Model Predictive Control. In: Magni, L., Raimondo, D.M., Allgöwer, F. (eds) Nonlinear Model Predictive Control. Lecture Notes in Control and Information Sciences, vol 384. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01094-1_33
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DOI: https://doi.org/10.1007/978-3-642-01094-1_33
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