Evgeny Lazutkin
Simulation and Optimal Processes Group, Institute for Automation and Systems Engineering, Technische Universität Ilmenau, Ilmenau, Germany.
Abebe Geletu
Simulation and Optimal Processes Group, Institute for Automation and Systems Engineering, Technische Universität Ilmenau, Ilmenau, Germany.
Siegbert Hopfgarten
Simulation and Optimal Processes Group, Institute for Automation and Systems Engineering, Technische Universität Ilmenau, Ilmenau, Germany.
Pu Li
Simulation and Optimal Processes Group, Institute for Automation and Systems Engineering, Technische Universität Ilmenau, Ilmenau, Germany.
Ladda ner artikel
http://dx.doi.org/10.3384/ecp14096999Ingår i: Proceedings of the 10th International Modelica Conference; March 10-12; 2014; Lund; Sweden
Linköping Electronic Conference Proceedings 96:104, s. 999-1006
This paper presents an efficient and a novel implementation of a combined multiple shooting and collocation (CMSC) algorithm for the solution of nonlinear optimal control problems. The implemented algorithm is a modification of the approach proposed in [17; 18]. The new implementation is done under the JModelica.org framework along with CasADi and Ipopt. The framework uses a symbolic pre-calculation of functions and derivatives. Besides the integration of various components of JModelica.org; Ipopt; and CasADi; the implementation facilitates simpler modeling of optimal control problems along with a choice of options for various linear algebra algorithms. The paper gives a description of the algorithm and elaborates the components of the framework. Numerical experimentations show that the new implementation is efficient in comparison with the published results of other authors.
Nonlinear Optimal Control; Symbolic
Automatic Differentiation; Nonlinear Programming; Multiple Shooting; Collocation
[1] Åkesson, J.: Optimica—An Extension of Modelica Supporting Dynamic Optimization. 6th International Modelica Conference, March 3 - 4, 2008, Bielefeld, Germany, pp. 57-66.
[2] Åkesson, J., Årzén, K.-E., Gåfvert, M., Bergdahl, T., Tummescheit, H.: Modeling and optimization with Optimica and JModelica.org-Languages and tools for solving large-scale dynamic optimization problems. Computers and Chemical Engineering, 34(2010)11, pp. 1737-1749.
[3] Andersson, J., et. al.: Dynamic optimization with CasADi. In Proceedings of the 51st IEEE Conference on Decision and Control, Maui (USA), 2012.
[4] J. Andersson, J., Casella, F., Diehl, M.: Integration of CasADi and JModelica.org. 8th International Modelica Conference, Dresden, 2011. DOI: 10.3384/ecp1106321
[5] Andersson, J., Åkesson, J., Diehl, M.: CasADi: A Symbolic Package for Automatic Differentiation and Optimal Control. Lecture Notes in Computational Science and Engineering, Vol. 87, Springer, 2012, pp. 297-307.
[6] Bachmann, B., Ochel, L., Ruge, V., Gebremedhin, M., Fritzson, P., Nezhadali, V., Eriksson, L., Sivertsson, M.: Parallel Multiple-Shooting and Collocation Optimization with OpenModelica. Proceedings of the 9th International Modelica Conference, Munich, pp. 659-668, 2012.
[7] Bartl, M., Li, P., Biegler, L. T.: Improvement of state profile accuracy in nonlinear dynamic optimization with the quasi-sequential approach. AIChE Journal, 57(2011)8, pp. 2185-2197.
[8] Biegler, L. T. Nonlinear Programming: Concepts, Algorithms, and Applications to Chemical Processes. SIAM, 2010.
[9] Bock, H. G., Plitt, K. J. A Multiple Shooting Algorithm for Direct Solution of Optimal Control Problems, Prepr. 9th IFAC World Congress, Budapest, 1984, pp. 242-247.
[10] Cuthrell, J. E., Biegler, L. T.: Simultaneous optimization and solution methods for batch reactor control profiles. Comput. Chem. Eng. 13(1989), pp. 49-62.
[11] Ferreau, H. J.: Model predictive control algorithms for applications with millisecond timescales. PhD Thesis, KU Leuven, 2011.
[12] Franke, R.: Formulation of dynamic optimization problems using Modelica and their efficient solution. 2nd International Modelica Conference, March 18 - 19, DLR, Oberpfaffenhofen, Germany, pp. 315 - 323.
[13] Hong, W., Wang, S., Li, P., Wozny, G., Biegler, L. T.: A quasi-sequential approach to large-scale dynamic optimization problems. AIChE Journal, 52(2006)1, pp. 255-268.
[14] Kirches, C., Wirsching, L., Bock, H. G., Schlöder, J. P.: Efficient Direct Multiple Shooting for Nonlinear Model Predictive Control on Long Horizons. J. Process Control, 22(2012), pp. 540-550.
[15] Magnusson, F.: Collocation Methods in JModelica. org. Master Thesis, Lund University, February 2012.
[16] Russel, R. D., Shampine, L. F.: A Collocation Method for Boundary Value Problems, Numerical Mathematic, 19(1971), pp. 1-28, Springer.
[17] Tamimi, J.: Development of the Efficient Algorithms for Model Predictive Control of Fast Systems. PhD Thesis, Technische Universität Ilmenau, VDI Verlag, 2011.
[18] Tamimi, J., Li, P.: A Combined approach to nonlinear model predictive control of fast systems. J. Process Control, 20(2010)9, pp. 1092-1102.
[19] Wächter, A., Biegler, L.T.: On the Implementation of a Primal-Dual Interior Point Filter Line Search Algorithm for Large-Scale Nonlinear Programming, Mathematical Programming, Ser. A, 106(2006)1, pp. 25-57.
