Summary
In accordance with the working plan of the project, the scientific and applied investigations are performed in the following directions:
(a) Development of algorithms and software tools for model-based study of bioprocesses. A program package for bifurcation analysis of continuous-time dynamical systems is developed and implemented in the computer algebra system Maple 13. A numerical model-based extremum seeking algorithm is established and realized in Maple 13. An interface for dynamic communication between the computer algebra system Mathematica and the C--XSC/CToolbox for verified solutions of practically important nonlinear problems is realized.
(b) Computer simulations and investigations of concrete bioprocess models. Several bench-mark biotechnological models are studied; the models are described by continuous-time dynamical systems. Established is the global asymptotic stability of the models by means of feedback control laws; the latter depend on on-line measurements only and are robust under model uncertainties. Thereby the algorithms and software tools from the previous item (a) are exploited. The problem of model-based optimization of the bioreactor (chemostat) is also solved. Computer simulation are carried out to demonstrate the theoretical studies. New theoretical results related to the theory of nonlinear control systems are also obtained like new sufficient conditions for local controllability, new necessary conditions for optimal control problems of Pontryagin's maximum principle type etc.
(c) Algorithms for solving uncertain problems. The investigations are devoted to the problem of describing the parametric solution set of an interval linear system. Developed are algorithms for describing this set for different classes of linear systems with different dimension. A procedure for the explicit description of the AE solution set is also established; the latter is closely related to an important problem in control theory. Theoretical results, concerning algebraic properties of interval operations, properties of quasilinear interval spaces, stochastic arithmetic, mathematical morphology are also obtained.
(d) Investigation of protein structures and functions. New algorithms for protein structure similarity are developed, which are more efficient with respect to their applicability to large-scale problems, optimality in computational time and computational resources.
The results are presented in 49 papers, including: 41 published papers (16 of them in journals with impact factor(IF)); 4 papers accepted for publication (3 of them in journals with IF); 4 papers submitted for publication, where the present project is acknowledged.
Members of the project team have delivered 61 talks on the subject of the project in international scientific workshops and conferences in Bulgaria and abroad; thereby 32 of the talks are delivered in the international events, organized by members of the project team.
Published Papers
- 1. R. Anguelov, E. Popova, Reliable Simulations for Applied Dynamical Models, in T.E. Simos et al. (Eds), Numerical Analysis and Applied Mathematics (7th International Conference ICNAAM 2009 Aquila Rithymna Beach, Rethymno, Crete, Greece, September 18-22, 2009), American Inst. of Physics Conference Proceedings 1168, Melville, New York, 2009, 1205-1208.
- 2. R. Anguelov, S. Markov, F. Minani: Hausdorff Continuous Viscosity Solutions of Hamilton-Jacobi Equations. In: I. Lirkov, S. Margenov, J. Wasniewski (eds.), Large-Scale Scientific Computing, Lecture Notes in Computer Science 5910, 241-248, 2010.
- 3. N. Dimitrova, M. Krastanov: Nonlinear Stabilizing Control of an Uncertain Bioprocess Model. Int. J. Appl. Math. Comput. Sci., 2009, Vol. 19, No. 3, 441-454., DOI: 10.2478/v10006-009-0036-0 (IF=0.684)
- 4. N. Dimitrova: Local Bifurcations in a Nonlinear Model of a Bioreactor. Serdica Journal of Computing, Vol. 3, No. 2, 2009, 107-132.
- 5. N. Dimitrova, M. Krastanov: Nonlinear Adaptive Control of a Model of an Uncertaim Fermentation Process. Int. J. Robust Nonlinear Control, 2010; 20:1001--1009. Published online September 2009 in Wiley InterScience (www.interscience.wiley.com), DOI: 10.1002/rnc.1503 (IF=1.108)
- 6. Said Hanafi, Nicola Yanev: Tabu search approaches for solving the two-group classification problem. Annals of Operations Research, Springer Science+Business Media, LLC 2009, DOI 10.1007/s10479-009-0581-9 (IF=0.619)
- 7. M. I. Krastanov, A Sufficient Condition for Small-Time Local Controllability, SIAM J. on Control & Optimization, Volume 48, Issue 4, 2296-2322, 2009. (IF=1.770)
- 8. M. I. Krastanov: High-order variations and small-time local attainability, Control and Cybernetics, vol. 38, Nr. 4, Part B, 1411-1428, 2009. (IF=0.495)
- 9. M. I. Krastanov, V. M. Veliov: High-order approximations to nonholonomic control systems, In: I. Lirkov, S. Margenov, J. Wasniewski (eds.), Large-Scale Scientific Computing, Lecture Notes in Computer Science 5910, 304-314, 2010.
- 10. N. Malod-Dognin, R. Andonov, Nicola Yanev: Maximum Clique in Protein Structure Comparison. 9th Intern. Symp. On Experimental Algorithms, 20--22 May 2010, Napoli, Italy. Lecture Notes in Comp. Sci., vol. 6049, 2010, 106-117.
- 11. E. Popova: Explicit Characterization of a Class of Parametric Solution Sets, Compt. rend. Acad. bulg. Sci., 62(10):1207-1216, 2009.
- 12. E. Popova, W. Kraemer, M. Russev: Integration of C-XSC Automatic Differentiation in Mathematica. PREPRINT Nr. 3/2010, IMI-BAS.
- 13. R. Alt, J.-L. Lamotte, S. Markov: Stochastic Arithmetic, Theory and Experiments. Serdica Journal of Computing, Vol. 4, Nr. 1, 2010, 1–10.
- 14. R. Alt, J.-L. Lamotte, S. Markov: On the accuracyof the solution of linear problems on the CELL processor. Reliable Computing 15, 2011, 1–12.
- 15. R. Alt, S. Markov: Theoretical and Computational Studies of Some Bioreactor Models. Computers and Mathematics with Applications, published on-line 2012, DOI: 10.1016/j.camwa.2012.0.046. (IF=1.472)
- 16. R. Andonov, N. Malod-Dognin, Nicola Yanev: Maximum Contact Map Overlap Revisited. Journal of Computational Biology, 18(1) 27–41, 2011; doi:10.1089/cmb.2009.0196. (IF=1.694)
- 17. R. Anguelov, S. Markov, F. Minani: Hausdorff Continuous Viscosity Solutions of Hamilton-Jacobi Equations. In: I. Lirkov, S. Margenov, J. Wasniewski (eds.), Large-Scale Scientific Computing, Lecture Notes in Computer Science 5910, 241–248, 2010.
- 18. R. Anguelov, E. Popova: Reliable Simulations for Applied Dynamical Models. In T. E. Simos et al. (Eds), Numerical Analysis and Applied Mathematics (7th International Conference ICNAAM 2009 Aquila Rithymna Beach, Rethymno, Crete, Greece, September 18-22, 2009), American Inst. of Physics Conference Proceedings 1168, Melville, New York, 2009, 1205–1208.
- 19. R. Anguelov, E. Popova: Topological structure preserving numerical simulations of dynamical models. J. Comp. Appl. Math. 235, 2010, 358–365. (IF=1.048)
- 20. M. Borisov, N. Dimitrova: One-Parameter Bifurcation Analysis of Dynamical Systems Using Maple. Serdica Journal of Computing, Vol. 4, Nr. 1, 2010, 43–56.
- 21. M. Borisov, N. Dimitrova: Stability analysis in a model of 1,2-dichloroethane biodegradation by Klebsiella oxytoca va 8391 immobilized on granulated activated carbon. In Proc. AMiTaNS'11, ed. M. D. Todorov, C. I. Christov, American Inst. of Physics AIP 1404, 284, 2011, 284–298; DOI: 10.1063/1.3659931.
- 22. M. Borisov, N. Dimitrova, V. Beschkov: Stability Analysis of a Biorector Model for Biodegradation of Xenobiotics. Computers and Mathematics with Applications, published on-line 2012, DOI: 10.1016/j.camwa.2012.0.067. (IF=1.472)
- 23. G. Collet, R. Andonov, N. Yanev, J.-F. Gibrat: Local Protein Threading by Mixed Integer Programming. Discrete Applied Mathematics 159, 2011, 1707–1716. (IF=0.894)
- 24. N. Dimitrova: Local Bifurcations in a Nonlinear Model of a Bioreactor. Serdica Journal of Computing, Vol. 3, No. 2, 2009, 107–132.
- 25. N. Dimitrova, M. Krastanov: Nonlinear Stabilizing Control of an Uncertain Bioprocess Model. Int. J. Appl. Math. Comput. Sci., 2009, Vol. 19, No. 3, 441–454. DOI: 10.2478/v10006-009-0036-0 (IF=0.684)
- 26. N. Dimitrova, M. Krastanov: Nonlinear Adaptive Control of a Model of an Uncertaim Fermentation Process. Int. J. Robust Nonlinear Control, 2010; 20:1001–1009; DOI: 10.1002/rnc.1503 (IF=1.108)
- 27. N. Dimitrova, M. Krastanov: Nonlinear Adaptive Control of a Bioprocess Model with Unknown Kinetics. In: Modeling, Design, and Simulation of Systems with Uncertainties (Mathematical Engineering), eds. A. Rauh, E. Auer, Chapter 13, 2011, 275–292.
- 28. N. Dimitrova, M. Krastanov: Adaptive asymptotic stabilization of a bioprocess model with unknown kinetics, Int. J. of Numerical analysis and modeling, Series B, Computing and Information, Volume 2, Nr. 2–3, 2011, 200–214.
- 29. N. Dimitrova, M. Krastanov: Nonlinear adaptive stabilizing control of an anaerobic digestion model with unknown kinetics, Int. J. Robust Nonlinear Control, 2011, published on-line, DOI 10.1002/rnc.1782. (IF=1.495)
- 30. N. Dimitrova, M. I. Krastanov: Adaptive asymptotic stabilization of a bioprocess model with unknown kinetics, Mathematica Balkanica, New Series, Vol. 25, Fasc. 3, 2011, 293–305.
- 31. N. Dimitrova, M. I. Krastanov, On the Asymptotic Stabilization of an Uncertain Bioprocess Model. In: I. Lirkov, S. Margenov, J. Wansiewski (Eds.): LSSC'2011, Lecture Notes in Computer Sciences, Springer, 7116, 2012, 115–122.
- 32. N. Dimitrova: Modeling the production of genetically modified organisms in the chemostat. Mathematica Balkanica, New Series, Vol.25, 2011, Fasc. 3, 277–291.
- 33. S. Hanafi, Nicola Yanev: Tabu search approaches for solving the two-group classification problem. Annals of Operations Research, 183, 2011, 25–46; DOI 10.1007/s10479-009-0581-9 (IF=0.675)
- 34. M. I. Krastanov: A Sufficient Condition for Small-Time Local Controllability, SIAM J. on Control & Optimization, Vol. 48, Issue 4, 2296–2322, 2009. (IF=1.770)
- 35. M. I. Krastanov: High-order variations and small-time local attainability. Control and Cybernetics, vol. 38, Nr. 4, Part B, 1411–1428, 2009. (IF=0.495)
- 36. M. Krastanov: High-Order Control Variations and Small-time Local Controllability. Serdica Journal of Computing, Vol. 4, Nr. 1, 2010, 85–92.
- 37. M. I. Krastanov, V. M. Veliov: High-order approximations to nonholonomic control systems. In: I. Lirkov, S. Margenov, J. Wasniewski (eds.), Large-Scale Scientific Computing, Lecture Notes in Computer Science 5910, 304–314, 2010.
- 38. M. I. Krastanov, N. K. Ribarska, Ts. Y. Tsachev: A Pontryagin maximum principle for infinite-dimensional problems, SIAM Journal of Control and Optimization, Issue 5, 2011, 2155–2182. (IF=1.517)
- 39. N. Malod-Dognin, R. Andonov, Nicola Yanev: Solving Maximum Clique Problem for Protein Structure Similarity. Serdica Journal of Computing, Vol. 4, Nr. 1, 2010, 93–100.
- 40. N. Malod-Dognin, R. Andonov, Nicola Yanev: Maximum Clique in Protein Structure Comparison. 9th Intern. Symp. On Experimental Algorithms, 20--22 May 2010, Napoli, Italy. Lecture Notes in Comp. Sci., vol. 6049, 2010, 106–117.
- 41. S. Markov, N. Hayes: On the Arithmetic of Errors. Serdica J. Computing, Vol. 4, 2010, 447–462.
- 42. S. Markov: Biomathematics and Interval Analysis: A Prosperous Marriage. In Proc. AMiTaNS'10, ed. M. D. Todorov, C. I. Christov, American Inst. of Physics, 2010, 26–36.
- 43. S. Markov: On the Mathematical Modelling of Microbial Growth: Some Computational Aspects. Serdica J. Computing 5, 2011, 153–168.
- 44. S. Markov: Intervals and (Non-)Negative Numbers. TR UPWT 2011/5, 1–18.
- 45. A. Popov: A New Approach to Fuzzy Arithmetic. Serdica Journal of Computing, Vol. 4, Nr. 1, 2010, 113–122.
- 46. E. Popova: Explicit Characterization of a Class of Parametric Solution Sets. Compt. rend. Acad. bulg. Sci., 62(10) 1207–1216, 2009. (IF=0.152)
- 47. E. D. Popova: Explicit Description of 2D Parametric Solution Sets, BIT Numerical Mathematics, 52, 179–200, 2012; published online June 2011, DOI 10.1007/s10543-011-0339-z. (IF=0.821)
- 48. E. Popova: Explicit Description of AE Solution Sets to Parametric Linear Systems. Preprint Nr. 7/2011, IMI–BAS.
- 49. E. D. Popova: The United Solution Set to 3D Linear System with Symmetric Interval Matrix. Proc. 6th Annual Meeting of Bulg. Sect. SIAM, December 21--22, 2011, 80–85.
- 50. E. Popova, W. Kraemer, M. Russev: Integration of C-XSC Automatic Differentiation in Mathematica. Preprint Nr. 3/2010, IMI–BAS.
- 51. E. Popova, W. Kraemer: Embedding C-XSC Nonlinear Solvers in MATHEMATICA, Compt. rend. Acad. bulg. Sci., (Compt. Rend. de l'Academie bulgare des Sciences) 64(1) 11–20, 2011. (IF=0.219)
- 52. E. Popova, W. Kraemer: Characterization of AE Solution Sets to a Class of Parametric Linear Systems. Compt. rend. Acad. bulg. Sci., (Comptes rendus de l'Academie bulgare des Sciences) 64(3), 325–-332, 2011. (IF=0.219)
- 53. N. Yanev, P. Milanov, I. Mirchev: Integer Programming Approach to HP Folding. Serdica J. Computing 5, 359–366, 2011.
- 54. A. T. Popov, S. A. Stoykov: Rough Sets in Biomedical Informatics. Accepted for publication in Biotechnology and Biotechnological Equipment, 2012. (IF=0.5)
- 55. Neli S. Dimitrova, Mikhail I. Krastanov: On the Asymptotic Stabilization of an Anaerobic Digestion Model with Unknown Kinetics. Accepted for publication in WSEAS Transactions on Systems, 2012.
- 56. M. I. Krastanov: On the Small-time Local Controllability. Accepted for publication in Journal of Convex Analysis, vol. 19, No. 4, 2012. (IF=0.911)
- 57. E. D. Popova, M. Hladik: Outer enclosures to the parametric AE solution set. Accepted for publication in Soft Computing, 2012. (IF=1.512)
- 58. M. Borisov: BifTools: Maple Package for Bifurcation Analysis of Dynamical Systems. Subm. to Journal of Symbolic Computations, 2012.
- 59. N. Dimitrova: On the Asymptotic Stabilization of a Chemostat Model of Plasmid-bearing, Plasmid-free Competition. Subm. to Proc. Intern. Conf. on Chaos and Complex Systems (CCS'2012), Antalya, Turkey, April 29 – May 2, 2012.
- 60. N. Dimitrova, M. Krastanov: Model-Based Biological Control of the Chemostat. Subm. to Proc. Intern. Conf. on Numerical Methods and Applications (NA&A'2012), June 2012, Lozenetz, Bulgaria.
- 61. M. Krastanov, M. Quincampoix: On the Small-Time Controllability of Discontinuous Piece-Wise Linear Systems. Submitted to Systems & Control Letters.
SERDICA JOURNAL OF COMPUTING, Vol. 4, Nr. 1, 2010
Special Issue of MMSC'2009, Velingrad, Bulgaria
Guest editors: N. Dimitrova, M. Krastanov
- 1. Rene Alt, Jean-Luc Lamotte, Svetoslav Markov:
Stochastic Arithmetic, Theory and Experiments, pp. 1-10.
- 2. M. Krastanov:
High-Order Control Variations and Small-time Local
Controllability, pp. 85-92.
- 3. M. Borisov, N. Dimitrova:
One-Parameter Bifurcation Analysis of Dynamical Systems
Using Maple, pp. 43-56
- 4. N. Malod-Dognin, R. Andonov, N. Yanev:
Solving Maximum Clique Problem for Protein Structure
Similarity, pp. 93-100
- 5. A. Popov:
A New Approach to Fuzzy Arithmetic, pp. 113-122.
Software - Maple 13 Packages