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Polish Information Processing Society
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Annals of Computer Science and Information Systems, Volume 8

Proceedings of the 2016 Federated Conference on Computer Science and Information Systems

The matrix-based description approach for the multistage differential-algebraic processes


DOI: http://dx.doi.org/10.15439/2016F493

Citation: Proceedings of the 2016 Federated Conference on Computer Science and Information Systems, M. Ganzha, L. Maciaszek, M. Paprzycki (eds). ACSIS, Vol. 8, pages 939942 ()

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Abstract. In the article a new insight into an optimal control problem of the multistage processes has been given. The multistage descriptor processes with differential-algebraic constraints are under considerations. The new representation of the descriptor model has been presented. Moreover, the new structures to represent the differential state variables, algebraic state variables, control function, as well the global parameters have been introduced. The generalized description enables the unified representation of a broad group of the multistage processes with differential-algebraic relations and indicates on the physical interpretation of the process variables.


  1. J. R. Banga, E. Balsa-Canto, C. G. Moles, A. A. Alonso. 2005. Dynamic optimization of bioprocesses: Efficient and robust numerical strategies. Journal of Biotechnology. 117:407-419, http://dx.doi.org/10.1016/j.jbiotec.2005.02.013
  2. J. T. Betts. 2010. Practical Methods for Optimal Control and Estimation Using Nonlinear Programming, Second Edition. SIAM, Philadelphia, http://dx.doi.org/10.1137/1.9780898718577
  3. L. T. Biegler. 2010. Nonlinear Programming. Concepts, Algorithms and Applications to Chemical Processes. SIAM, Philadelphia, http://dx.doi.org/10.1137/1.9780898719383
  4. L. T. Biegler. 2014. Nonlinear programming strategies for dynamic chemical process optimization. Theoretical Foundations of Chemical Engineering. 48:541-554, http://dx.doi.org/10.1134/S0040579514050157
  5. L. T. Biegler, S. Campbell, V. Mehrmann. 2012. DAEs, Control, and Optimization. Control and Optimization with Differential-Algebraic Constraints. SIAM, Philadelphia, http://dx.doi.org/10.1137/9781611972252.ch1
  6. K. E. Brenan, S. L. Campbell, L. R. Petzold. 1996. Numerical Solution of Initial- Value Problems in Differential-Algebraic Equations. SIAM, Philadelphia, http://dx.doi.org/10.1137/1.9781611971224
  7. M. Diehl, H. G. Bock, J. P. Schlöder, R. Findeisen, Z. Nagy, F. Allgöwer. 2002. Real-time optimization and nonlinear model predictive control of processes governed by differential-algebraic equations. Journal of Process Control. 12:577-585, http://dx.doi.org/10.1016/S0959-1524(01)00023-3
  8. P. Dra̧g, K. Styczeń. 2012. A Two-Step Approach for Optimal Control of Kinetic Batch Reactor with electroneutrality condition. Przeglad Elektrotechniczny. 6/2012, pp. 176-180.
  9. S. Drozdek, U. Bazylińska. 2016. Biocompatible oil core nanocapsules as potential co-carriers of paclitaxel and fluorescent markers: preparation, characterization, and bioimaging. Colloid and Polymer Science. 294:225-237, http://dx.doi.org/10.1007/s00396-015-3767-5
  10. S. Fidanova, M. Paprzycki, O. Roeva. 2014. Hybrid GA-ACO algorithm for a model parameters identification problem. Proceedings of the 2014 Federated Conference on Computer Science and Information Systems pp. 413420, http://dx.doi.org/ 10.15439/2014F373
  11. S. Fidanova, O. Roeva. 2013. Metaheuristic techniques for optimization of an E. coli cultivation model. Biotechnology and Biotechnological Equipment. 27:3870-3876, http://dx.doi.org/10.5504/BBEQ.2012.0136
  12. P. S. Harvey Jr, H. P. Gavin, J.T. Scruggs. 2013. Optimal performance of constrained control systems. Smart Materials and Structures. 21:085001, http://dx.doi.org/10.1088/0964-1726/21/8/085001
  13. M. Kwiatkowska. 2015. DAEs method for time-varying indoor air parameters evaluation. In: A. Kotowski, K. Piekarska, B. Kaźmierczak (eds.) Interdyscyplinarne zagadnienia w inżynierii i ochronie środowiska T. 6. Wrocław 2015, pp. 214-220.
  14. M. Kwiatkowska, A. Szczurek, P. Dra̧g. 2016. Zastosowanie równań różniczkowo-algebraicznych do predykcji zmian parametrów powietrza wewnȩtrznego. Przeglad Elektrotechniczny. 5/2015, pp. 181-184, http://dx.doi.org/10.15199/48.2016.05.34
  15. K. Matyja, A. Małachowska-Jutsz, A. Mazur, K. Grabas. Assessment of toxicity using dehydrogenases activity and mathematical modeling. Ecotoxicology. 25:924-939, http://dx.doi.org/10.1007/s10646-016-1650-x.
  16. V. S Vassiliadis, R. W. H. Sargent, C. C. Pantelides. 1994. Solution of a Class of Multistage Dynamic Optimization Problems. 1. Problems without Path Constraints. Ind. Eng. Chem. Res. 33:2111-2122, http://dx.doi.org/10.1021/ie00033a014
  17. V. S Vassiliadis, R. W. H. Sargent, C. C. Pantelides. 1994. Solution of a Class of Multistage Dynamic Optimization Problems. 2. Problems with Path Constraints. Ind. Eng. Chem. Res. 33: 2123-2133, http://dx.doi.org/10.1021/ie00033a015
  18. Z.-H. Yang, W.-J. Cui, Y. Tang. 2008. Optimal control with DAE constraints. International Conference on Industrial Engineering and Engineering Management, 2008. pp. 188-192, http://dx.doi.org/10.1109/IEEM.2008.4737857
  19. Z.H. Yang, F. Guo. 2012. Optimal Control Conditions with Differential-Algebraic Equation Constraints. Advanced Science Letters. 6:654-659, http://dx.doi.org/10.1166/asl.2012.2300