Dynamic Optimisation

This research concerns determination of the optimal open-loop and/or closed-loop control trajectories or parameter estimation. The systems under study are described by a system of nonlinear differential and algebraic equations. The optimal control and estimation methods developed are from the family of the called Control Vector Parametrisation and Orthogonal Collocation methods. The original continuous control vector is parametrised as a linear function of some basis functions. States remain continuous for CVP and are also parametrised in OC. Thus, the original dynamic optimisation problem is transformed into a static optimisation problem. Gradient and nongradient methods have been developed.

Analytic and numeric methods are investigated for optimal operation of batch membrane filtration processes. We have derived analytical solutions for minimum time and minimum diluant consumption problems containing optimal state curves as special cases of singular control trajectories. The analytical solutions have been confirmed numerically. The obtained results show that existing methods of membrane operation are close to optimal but there are cases when the proposed approach yields improved operation and profit.

Deterministic global methods in dynamic optimisation are investigated using rigorous approach of convex underestimators. The original nonconvex NLP problem is then solved usign a spatial branch-and-bound method to global optimality. Problems solved include global NMPC and global parameter estimation.

People in Group

• Associate professor: Radoslav Paulen (established his own group),
• Students:

Former colleagues: T. Hirmajer (PhD 2007), M. Podmajerský (PhD 2011), M. Jelemenský (PhD 2016), A. Sharma (PhD 2020), M. Čižniar, D. Pakšiová.

Software Packages

DYNO

A FORTRAN F77 package for dynamic optimisation that can deal with ODE systems subject to a general set of constraints using CVP.

dynopt

A MATLAB package for dynamic optimisation. It is based on total discretisation with orthogonal collocations on finite elements.

DOTcvp

A MATLAB package for dynamic optimisation. It is based on control vector parametrisation and gradients are calculated using sensitivity equations.

Journals

• R. Paulen, M. Fikar: Dynamic real-time optimization of batch processes using Pontryagin’s minimum principle and set-membership adaptation. Computers & Chemical Engineering, 128, 488–495, 2019. https://dx.doi.org/10.1016/j.compchemeng.2019.06.027.
• R. Paulen – M. Fikar: Dual-Control-Based Approach to Batch Process Operation under Uncertainty Based on Optimality-Conditions Parametrization. Industrial & Engineering Chemistry Research, 58 (30), 13508–13516, 2019. https://dx.doi.org/10.1016/10.1021/acs.iecr.9b00638.
• A. Sharma, R. Valo, M. Kalúz, R. Paulen, M. Fikar: Implementation of optimal strategy to economically improve batch membrane separation. Journal of Process Control, 76, 155–164, 2019. https://dx.doi.org/10.1016/j.jprocont.2019.02.001.
• Sharma, A., Jelemenský, M., Paulen, R., Fikar, M.: Modeling and optimal operation of batch closed-loop diafiltration processes, Chemical Engineering Research and Design, 122, 198-210, 2017. https://doi.org/10.1016/j.cherd.2017.04.016.
• Jelemenský, M., D. Pakšiová, Paulen, R., Latifi, A., Fikar, M.: Combined Estimation and Optimal Control of Batch Membrane Processes, Processes, 4(4), 43, 2016. http://www.mdpi.com/2227-9717/4/4/43, more
• Jelemenský, M., Paulen, R., Fikar, M., Kovács, Z.: Time-Optimal Operation of Multi-Component Batch Diafiltration. Computers & Chemical Engineering, 83, 131–138, 2015. http://http://dx.doi.org/10.1016/j.compchemeng.2015.05.029, more
• Paulen, R., Jelemenský, M., Kovács, Z., Fikar, M.: Economically optimal batch diafiltration via analytical multi-objective optimal control, Journal of Process Control, 28, 73-82, 2015. http://http://dx.doi.org/10.1016/j.jprocont.2015.02.008, more
• Paulen, R., Benyahia, B., Latifi, M.A., Fikar, M.: Analysis of optimal operation of a fed-batch emulsion copolymerization reactor used for production of particles with core-shell morphology, Computers and Chemical Engineering, 66, 233-243, 2014. http://dx.doi.org/10.1016/j.compchemeng.2014.02.021. more
• Podmajerský, M., Fikar, M., Chachuat, B.: Measurement-based optimization of batch and repetitive processes using an integrated two-layer architecture, Journal of Process Control, 23(7), 943-955, 2013. http://dx.doi.org/10.1016/j.jprocont.2013.05.003. more
• Paulen, R., Jelemenský, M., Fikar, M., Kovács, Z.: Optimal balancing of temporal and buffer costs for ultrafiltration/diafiltration processes under limiting flux conditions, Journal of Membrane Science, 444, 87-95, 2013, http://dx.doi.org/10.1016/j.memsci.2013.05.009. more
• Paulen, R., Fikar, M., Foley, G., Kovács, Z., Czermak, P.: Optimal feeding strategy of diafiltration buffer in batch membrane processes, Journal of Membrane Science, 411-412, 160-172, 2012, http://dx.doi.org/10.1016/j.memsci.2012.04.028. more
• Paulen, R., Foley, G., Fikar, M., Kovács, Z., Czermak, P.: Minimizing the process time for ultrafiltration/diafiltration under gel polarization conditions, Journal of Membrane Science, 380, 148-154, 2011, http://dx.doi.org/10.1016/j.memsci.2011.06.044. more
• Paulen, R., Fikar, M., Kovács, Z., Czermak, P.: Process optimization of diafiltration with time-dependent water adding for albumin production, Chemical Engineering and Processing: Process Intensification, 2011, 50, 815-821, 2011, http://dx.doi.org/10.1016/j.cep.2011.05.010. more
• Fikar, M., Kovács, Z., Czermak, P.: Dynamic optimization of batch diafiltration processes, Journal of Membrane Science, 2010, 355(1-2), 168–174, http://dx.doi.org/10.1016/j.memsci.2010.03.019. more, open access.
• Kovács, Z., Fikar, M., Czermak, P.: Mathematical modeling of diafiltration, Hungarian Journal of Industrial Chemistry, 2009, 37(2), 159-164. more, open access.
• Čižniar, M., Podmajerský, M., Hirmajer, T., Fikar, M., Latifi, M. A.: Global optimization for the parameter estimation of differential-algebraic systems, Chemical Papers, 63(3), 274-283, 2009. more
• Fikar, M., T. Hirmajer: Optimal Control of a Two-Stage Reactor System. Chemical Papers, 60(5), 381-387, 2006. more
• T. Hirmajer, M. Fikar: Optimal Control of a Hybrid Coupled Tanks System. Journal of Electrical Engineering 2006, 57 (3), 166-171. more
• Fikar, M., Chachuat, B., Latifi, M. A.: Optimal operation of alternating activated sludge processes. Control Engineering Practice 13(7), 853-861, 2005. more
• Fikar, M., Latifi, M. A., Corriou, J.-P., Creff, Y.: CVP-Based Optimal Control of an Industrial Depropanizer Column. Computers chem. Engng., 24, 909-915, 2000. more
• Fikar, M., Latifi, M. A., Creff, Y.: Optimal Changeover Profiles for an Industrial Depropanizer. Chem. Eng. Sci., 54(13-14), 2715-2720, 1999. more
• Latifi, M. A., Corriou, J.-P., Fikar, M.: Dynamic optimisation of chemical processes. Trends in Chemical Engineering, 4, 189-201, 1998. Abstract
• Fikar, M., Latifi, M. A., Fournier, F., Creff, Y.: Application of Iterative Dynamic Programming to Optimal Control of a Distillation Column. Can. J. Chem. Eng., 76(12), 1110-1117, 1998. more
• Fournier, F., Fikar, M., Latifi, M. A.: Control Vector Parametrization in Optimal Control of a Batch Electrochemical Reactor. Chem. Biochem. Eng. Q., 12, 81-85, 1998. more
• Fikar, M., Latifi, M. A., Fournier, F., Creff, Y.: CVP versus IDP in Dynamic Optimisation of a Distillation Column. Computers chem. Engng., 22, S625-S628, 1998. more

Conferences

• Jelemenský, M., Paulen, R., Fikar, M., Kovacs, Z.: Economically Optimal Control of Batch Diafiltration Processes. IEEE Multi-Conference on Systems and Control, Hyderabad, India, 734–739, 2013. more
• Jelemenský, M., Paulen, R., Fikar, M., Kovacs, Z.: Multi-objective optimal control of ultrafiltration/diafiltration processes. Proceedings of the 12th European Control Conference, Zurich, Switzerland, 3384–3389, 2013. more
• Paulen, R., Fikar, M., Kovacs, Z., Czermak, P.: Time-optimal batch diafiltration. 8th International Symposium on Advanced Control of Chemical Processes ADCHEM 2012 Singapore, 10-13 July 2012, 804–809, 2012. more
• Paulen, R., Fikar, M., Kovacs, Z., Czermak, P.: Optimal Control of Diafiltration Process for Albumin Production. Preprints of the 18th IFAC World Congress Milano (Italy) August 28 - September 2, 2011, 14007–14012, 2011. more
• Fikar, M.: Optimal operation of dynamic processes. Editors: Markoš, J., In: Proceedings of the 37th International Conference of Slovak Society of Chemical Engineering, Tatranske Matliare, Slovakia, 3-15, 2010. more Presentation slides [PDF]
• Čižniar, M., Fikar, M., Latifi, M. A.: Design of constrained nonlinear model predictive control based on global optimisation. Editors: B. Braunschweig and X. Joulia, 18th European Symposium on Computer Aided Process Engineering, Lyon, France, 563-568, 2008. more
• Hirmajer, T., Čižniar, M., Fikar, M.: Application of a Gradient Method to Dynamic Optimization Problems. In: Proc. 16. Int. Conference Process Control '07, Štrbské Pleso, High Tatras, Slovakia, 023f.pdf, 2007. more
• Podmajerský, M., Čižniar, M., Hirmajer, T., Fikar, M., Latifi, M. A.: Recent Developments in Dynopt Package. In: Proc. 16. Int. Conference Process Control '07, Štrbské Pleso, High Tatras, Slovakia, 032f.pdf, 2007. more
• T. Hirmajer, M. Fikar: Optimal Control of a Hybrid Coupled Tanks System. Cybernetics and Systems 2006, 41-45, Vienna, Austria, 2006. more
• Čižniar, M., Salhi, D., Fikar, M., Latifi, M. A.: DYNOPT - Dynamic Optimisation Code for MATLAB. Proceedings of Technical Computing Prague 2005, cizniar.pdf, 2005. Poster (PDF), more
• Fikar, M., Calik, K.: Automatic Differentiation with DYNO. Proceedings of the 15th Int. Conference Process Control '05, Štrbské Pleso, June 7--10, 2005, Slovakia. CD-ROM Proceedings, 209f.pdf. more
• M. Čižniar, D. Salhi, M. Fikar, and M.A. Latifi: A MATLAB Package for Orthogonal Collocations on Finite Elements in Dynamic Optimisation. Proceedings of the 15th Int. Conference Process Control '05, Štrbské Pleso, June 7--10, 2005, Slovakia. CD-ROM Proceedings, 058f.pdf. more
• Fikar, M., Chachuat, B., Latifi, M. A.: Dynamic Optimisation of Alternating Activated Sludge Processes. CD ROM Proceedings of the European Control Conference 2003, 1-4 September 2003, University of Cambridge, UK, File 536.pdf. more Poster:PDF
• Fikar, M., Latifi, M. A., Creff, Y.: Dynamic Optimization of a highly nonlinear Depropanizer. CD-ROM Proceedings of CHISA'98, Paper No. 1207, August 23-28, 1998, Prague, Czech Republic. Abstract, Presentation:PS.ZIP, Article:PS.ZIP
• Fikar, M., Latifi, M. A., Fournier, F., Creff, Y.: CVP versus IDP in Dynamic Optimisation of a Distillation Column. Computers chem. Engng./ ESCAPE 8, 22, S625-S628, 1998. Abstract, Poster:PS.ZIP
• Fikar, M., Latifi, M. A., Fournier, F., Creff, Y.: Optimal Control of a Distillation Column Using Iterative Dynamic Programming. Proceedings 11th Conference Process Control'97, Tatranske Matliare, 236 - 240, 1997. Abstract, Article:PS.ZIP

Reports

• Hirmajer, T., Fikar, M., Balsa-Canto, E., Banga, J.R.: DOTcvp: Dynamic Optimization Toolbox with Control Vector Parameterization approach. Radlinského 9, 812 37 Bratislava 1, Slovak Republic, (Available at: hirmajer/dotcvp.html), 2007. more
• Paulen, R.: Global Optimization of Processes. Master Thesis, ÚIAM FCHPT STU in Bratislava, 2008. more
• Podmajerský, M.: Parameter Estimation in Processes from Experimental Data. Master Thesis, ÚIAM FCHPT STU in Bratislava, 2007. more
• Hirmajer, T., Fikar, M.: Solution of Dynamic Optimization Problems with Sensitivity Equations Approach. Technical Report, OIRP FCFT STU, Bratislava, Slovakia, 2007. more
• M. Fikar, M. A. Latifi, User's Guide for FORTRAN Dynamic Optimisation Code DYNO, Technical Report MF0201, LSGC CNRS, Nancy, France; STU Bratislava, Slovak Republic, 2002. Abstract, PDF
• M. Fikar, On Inequality Path Constraints in Dynamic Optimisation, Technical Report MF0102, Laboratoire des Sciences du Genie Chimique, CNRS, Nancy, France, 2001. Abstract, PDF
• M. Fikar, Dynamic Optimisation of Small-size Wastewater Treatment Plants, MF0101, Laboratoire des Sciences du Genie Chimique, CNRS, Nancy, France, Final report of the program: Accueil de chercheur etranger de haut niveau, Ministere de la recherche, 2001. Abstract, PDF