Conference article

Using Modelica models in real time dynamic optimization - gradient computation

Pål Kittilsen
Cybernetica AS, Norway

Lars Imsland
Cybernetica AS, Norway

Tor Steinar Schei
Cybernetica AS, Norway

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Published in: Proceedings of the 7th International Modelica Conference; Como; Italy; 20-22 September 2009

Linköping Electronic Conference Proceedings 43:88, s. 748-756

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Published: 2009-12-29

ISBN: 978-91-7393-513-5

ISSN: 1650-3686 (print), 1650-3740 (online)


This paper reports on implementation of gradient computation for real-time dynamic optimization; where the dynamic models can be Modelica models. Analytical methods for gradient computation based on sensitivity integration is compared to finite difference-based methods. A case study reveals that analytical methods outperforms finite difference-methods as the number of inputs and/or input blocks increases.


Nonlinear Model Predictive Control; Sequential Quadratic Programming; Gradient computation; Offshore Oil and Gas Production


[1] L. T. Biegler; A. M. Cervantes; and A. Wächter. Advances in simultaneous strategies for dynamic process optimization. Chem. Eng. Sci.; 57:575–593; 2002. doi: 10.1016/S0009-2509(01)00376-1.

[2] H. G. Bock; M. Diehl; D. B. Leineweber; and J. P. Schlöder. A direct multiple shooting method for real-time optimization of nonlinear DAE processes. In F. Allgöwer and A. Zheng; editors; Non-linear Predictive Control; volume 26 of Progress in Systems Theory; pages 246–267. Birkhäuser; Basel; 2000.

[3] N. M. C. de Oliveira and L. T. Biegler. An extension of newton-type algorithms for nonlinear process control. Automatica; 31:281–286; 1995. doi: 10.1016/0005-1098(94)00086-X.

[4] B. A. Foss and T. S. Schei. Putting nonlinear model predictive control into use. In Assessment and Future Directions Nonlinear Model Predictive Control; LNCIS 358; pages 407–417. Springer Verlag; 2007.

[5] E. Hairer; S. P. Nørsett; and G. Wanner. Solving Ordinary Differential Equations I – Nonstiff problems. Springer-Verlag; 2nd edition; 1993.

[6] A. C. Hindmarsh and R. Serban. User Documentation for CVODES v2.5.0. Center for Applied Scientific Computing; Lawrence Livermore National Laboratory; 2006.

[7] L. Imsland; P. Kittilsen; and T. S. Schei. Modelbased optimizing control and estimation using modelica models. In Proc. of Modelica’2008; Bielefeld; Germany; 2008.

[8] J. B. Jørgensen. Adjoint sensitivity results for predictive control; state- and parameter-estimation with nonlinear models. In Proceedings of the European Control Conference; Kos; Greece; 2007.

[9] J. M. Maciejowski. Predictive Control with Constraints. Prentice-Hall; 2001.

[10] J. Nocedal and S. J. Wright. Numerical Optimization. Springer-Verlag; New York; 2006.

[11] S. J. Qin and T. A. Badgwell. A survey of industrial model predictive control technology. Control Engineering Practice; 11:733–764; 2003. doi: 10.1016/S0967-0661(02)00186-7.

[12] T. S. Schei. On-line estimation for process control and optimization applications. Journal of Process Control; 18:821–828; 2008. doi: 10.1016/j.jprocont.2008.06.014.

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